{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fqp93JixVuiN"
      },
      "source": [
        "##### Copyright 2020 The TensorFlow Probability Authors.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "MeKZo1dnV1cE"
      },
      "outputs": [],
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DcriL2xPrG3_"
      },
      "source": [
        "# TensorFlow Probability on JAX\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://www.tensorflow.org/probability/examples/TensorFlow_Probability_on_JAX\"><img src=\"https://www.tensorflow.org/images/tf_logo_32px.png\" />View on TensorFlow.org</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/TensorFlow_Probability_on_JAX.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/TensorFlow_Probability_on_JAX.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a href=\"https://storage.googleapis.com/tensorflow_docs/probability/tensorflow_probability/examples/jupyter_notebooks/TensorFlow_Probability_on_JAX.ipynb\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\" />Download notebook</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pbgRDzCar7WY"
      },
      "source": [
        "TensorFlow Probability (TFP) is a library for probabilistic reasoning and statistical analysis that now also works on [JAX](https://github.com/google/jax)! For those not familiar, JAX is a library for accelerated numerical computing based on composable function transformations.\n",
        "\n",
        "TFP on JAX supports a lot of the most useful functionality of regular TFP while preserving the abstractions and APIs that many TFP users are now comfortable with."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yCaBElaf0soq"
      },
      "source": [
        "## Setup"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bF_03uaV1ubC"
      },
      "source": [
        "TFP on JAX does **not** depend on TensorFlow; let's uninstall TensorFlow from this Colab entirely."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dQMyDsSckCpV"
      },
      "outputs": [],
      "source": [
        "!pip uninstall tensorflow -y -q"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RWuX9PEH1lnp"
      },
      "source": [
        "We can install TFP on JAX with the latest nightly builds of TFP."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Tl5CfrtVkQd7"
      },
      "outputs": [],
      "source": [
        "!pip install -Uq tfp-nightly[jax] > /dev/null"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9KmtUvMH9hYg"
      },
      "source": [
        "Let's import some useful Python libraries."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oEQyYGq03SM_"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ]
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "from sklearn import datasets\n",
        "sns.set(style='white')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w1bCh_GA1pxo"
      },
      "source": [
        "Let's also import some basic JAX functionality."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "pSa7v4CWk38v"
      },
      "outputs": [],
      "source": [
        "import jax.numpy as jnp\n",
        "from jax import grad\n",
        "from jax import jit\n",
        "from jax import random\n",
        "from jax import value_and_grad\n",
        "from jax import vmap"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "53T-n_PM11Mf"
      },
      "source": [
        "## Importing TFP on JAX\n",
        "\n",
        "To use TFP on JAX, simply import the `jax` \"substrate\" and use it as you usually would `tfp`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nlx8w2gPkEM6"
      },
      "outputs": [],
      "source": [
        "from tensorflow_probability.substrates import jax as tfp\n",
        "tfd = tfp.distributions\n",
        "tfb = tfp.bijectors\n",
        "tfpk = tfp.math.psd_kernels"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jQ-FGn2hje8b"
      },
      "source": [
        "## Demo: Bayesian logistic regression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-xJm7Q5YkD_3"
      },
      "source": [
        "To demonstrate what we can do with the JAX backend, we'll implement Bayesian logistic regression applied to the classic Iris dataset.\n",
        "\n",
        "\n",
        "First, let's import the Iris dataset and extract some metadata.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0HHsy5lsf_S7"
      },
      "outputs": [],
      "source": [
        "iris = datasets.load_iris()\n",
        "features, labels = iris['data'], iris['target']\n",
        "\n",
        "num_features = features.shape[-1]\n",
        "num_classes = len(iris.target_names)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9pXr2atnk8xA"
      },
      "source": [
        "We can define the model using `tfd.JointDistributionCoroutine`. We'll put standard normal priors on both the weights and the bias term then write a `target_log_prob` function that pins the sampled labels to the data."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0Ri7RxnekWUr"
      },
      "outputs": [],
      "source": [
        "Root = tfd.JointDistributionCoroutine.Root\n",
        "def model():\n",
        "  w = yield Root(tfd.Sample(tfd.Normal(0., 1.),\n",
        "                            sample_shape=(num_features, num_classes)))\n",
        "  b = yield Root(\n",
        "      tfd.Sample(tfd.Normal(0., 1.), sample_shape=(num_classes,)))\n",
        "  logits = jnp.dot(features, w) + b\n",
        "  yield tfd.Independent(tfd.Categorical(logits=logits),\n",
        "                        reinterpreted_batch_ndims=1)\n",
        "\n",
        "\n",
        "dist = tfd.JointDistributionCoroutine(model)\n",
        "def target_log_prob(*params):\n",
        "  return dist.log_prob(params + (labels,))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A-U0hmnIlQM9"
      },
      "source": [
        "We sample from `dist` to produce an initial state for MCMC. We can then define a function that takes in a random key and an initial state, and produces 500 samples from a No-U-Turn-Sampler (NUTS). Note that we can use JAX transformations like `jit` to compile our NUTS sampler using XLA."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PBYkURyakn3c"
      },
      "outputs": [
        {
          "data": {
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lyhT86le/Qm1trfT8zZs3o7q6mv1dVVWFmpqavLa5M4AXGl5zVf5SzvADTjTV8PckTWpg3wqMGT4g577+KR9ORqbJDB1kEdT3PrkKZ133Qk7bkS/wk6JUk2FCRsfilRvbdI9GbpKU9RO/3GU7drWib4/SnOVLa036JzhtD0h4RSKaayGWrZAROZnFKzdi0XvfYP4bX4RKvCp7Jo9HpuSxmwJiafwgPhu/QGGBuwVwEy+YuezUU0/Fpk2bpPuWLFmCGTNmoG/fvlBVFU8//TQuvPBCLFq0CJqmYdasWaiqqoKu6/jHP/6BK664Ao899lihmt4hyMYeHZS7TNdNRCPO71yCOmpaN9jkIq5kKU6GoCi5LxTlDsZ0rs0PoOFDeuGyHx2KyvJYTu9dCPDfNMGZa+i70+SRSOrYXt+2QNtGbqUs63vkRSXuSiR1xGMaIlqO4mQ4c1kuF0XMMcVwlwAXzV+8eRkANm9rgqYp6NezzD5eLpT+8/Ia698tJ6GMMz2KkCl64mPK3mFTG2ohidwn71VHi5VC5DosmCYzf/58vPvuu9J/mqahf//+UG03pGnTpqG5uZlpIVVVVQAATdPw4x//GKtWrXKt0AlVVVUuQbZ582YMGDCgAE/nwDRNvPHBt+22+fMfP9OkHChkJLmu2gMZ8dwaMDGYhulyYVZVJefpQmQBioBAoCoKBvatyLnTQSHAP59Mk6G+lkjpgdHjQWhoTqLaNmPKJjnDp55MMqUjFtU4TaZtfYzqyCQCcs+1B3ywsCtORhAazcJkfvFti/C/N7/se7yIppZgYRBGk+GPaY/OL8Y73XDfO/hyYz0ATpMpQJmQTmMu401gixcvhqqq6N+/P9LpNLZtc9I4PP/889hvv/2YQOIxadIkPPHEEzAMAzt27MCiRYtwwgknFKT9hA/XbcOdc5fjwQUft+s6vNlr49ZGPPzfT30HnUuQ6EFCpv0dSuaZw+eb8sTJSDSZ9qrorYk0rr9vKdZvcg8Y8Tc/eA/cuzeA/LlR5xOGj5AhToa2ydyyefNTEBqbk6juW4HKipi0n6RZnIzQNhOIRVWHk2njpHXjfUtx2lUL8paFmd5NWg8WMjt2BWuCmYRoMoNTjZT4D2EuawtkC6rZdknu3dJclglXXXUVtm/fDkVRUFFRgdmzZyMSiaC5uRkXX3wxUilLne/Xrx/+9Kc/sfMuuugiXHbZZRg5ciSmTp2KVatW4fjjjwcA/OIXv8DgwYML+hy0ktnWzpTc/ED/9T2L0diSwklH7YXelaWeY5MBA5PXXnhTkmgWCIu0ZEIP0mQMA4KQUdo9ebzzcQ0++GwLSmMRXP0/o33Tyhimie7lMfzhF0ejum8Fu38souYl60G+wH/DtVzWX1qI0LPItOcnX12L8yYdkPEeDc0pDOrfDZqq+HAyck0GsDy2SJNpq7ZMbrateUqQ6W8uM1z9MZMmmEmTyRR/JSX+hY25NifzICcAeo5CmMs6jZCZM2eOdHtZWRnmzZvne959993HfmuahhtvvDHXTSsofnrzQhxx4ACcNXF/to1IWb++x08u4iDnV5aGIHCikbZED3sndBpYEU31mDF5F2bAik5v7yBau2EnAGBIdXdXO1RFJP4tATe4fzfX+bGo1sWEjPO+nntrPfud1k2Ypsnef0IoX1BZEcO6b+tD3aOhOYluZTGoqurjXSYn/gEgGtFYJHt7if9kSmeCLpcTIM9B8M8nlgPPtADKJGRoLDa3pqTcTCjiP2QGD7pfY3NSuviUPQtF+pPG9dXmXfjsqx0YtlevwPu0B13PdtDJQfNpW+fRrTtb8Nxb6+UmC58OF0SWuvkKf8IzLGSmKfq/NK75uDA7f1vmsjbdmoEmThrEaXb/iCdORhaTE4t2rW7vN/HpuuH6HmKeu0H9urE6P0FI6waaW9PoVhqFqipSbSSo/HI8qiKiEvHfPuHdkkgzLiFXK3rTNJlDhGgu29WUdD1vJsGWKcI/mdLxzJvr8KNrX5CWSg5nLpMLmUH9LG28otQRXjff/y4uuGmhtC1BpjDqN00tKfz6L4t9j8sFutZo6wKgOc1E+waIzLbtNwCSKZ0JNy8nIx9Aad3KZ/ToS59lNZhlpinqsPFYxDfVP8Ei/tv+bu57+kMWmU3XoXaUxCNuc5khNwnGo44Cn0/TBGF7fYurYme28PvuacN0mWdEITOwbwVqtjdnjPynGI9u5TFoqiL1gAoqvxyL5k6TaWhOsbQ2ueILtte3snejGwbL7RbRVDQ0J11jxu9dz/jzG3jpna8zpqFJpgw8bWdVlsXO8I906/SxGNSvgrVHdgy/iBhSXYmpP9jHNaYpNU0YDYmH1705f8HJRSGTY9Ck1t7xIVtN+moyKZ3lIJK5MBMMV9Cijt/9YwkeW/h5VoFesuwC1EFL45pXyAnEv6oo7dJknl38Jft93zMf4T8vf84Gfkks4ho8pilPKFha4giZ9k6KYXDBTQtx/g1tDwr2ExKGYTKzn6p4+8egfhXQDRNbdgbzg8RDVJTFoCrBmoxpeic0y7uMiP/2aTKNzUkWIGhmcSnTNLF4xUZprIqbx3I0mR4VMUvIhDCXfbGhDn99YmUoTmabrTXJrsQLznhUg6p6OUrDx/oQj2qIaIq0DVKPQJ9n4U2sBD6vWa5RFDK5Ro7iDPmV75jhlhv2nY8sx5Qrn/Ecm0wZKLOFjIcT4Tus0HnJPhsmiMw5z63JfPzldvy/fy4FYGkyfqn+Ce2Jk5Gd98iLn3HmMg0r12xl5aUNH3MZb25o76RYCPgJZYPTZCrKvPE/lFmBUoj4gWJkupVFoWly4t/tNOLeF7MnP6D9RHJaN5m5TFzhB2HV2q2Y9cj7mPvSZ559tULlTiZkusXR0JRy9YFM/SGdwczs8v6TCAP+keJRzVp0BZjLeJTENEQjGuPieMg0LL/rkLs4j41bi0LmOwdaWVxw8nCccOSeACySToZEUmer88A4GYGTIYHR3EYhk0obrhQmJTHNG4wpmssUxVOTJCz8VpG0nYTZLXaNDD8POj7zbLap2jsCfhOfbpiMaO5W5iWZKYBwW12wW+4uW5PpZmsy8lWx22uPRzyqMRfmbDTDDbUN0vLFbeFkvq6xUtnL+ggrYRBRoeuOd1llRRwNzUl3xowcEf+A3PLAP1OMNJkAcxmPeExjLviebNCS9+6nyby09CuPJsML4lyjKGRyDMbJ+PSU9ZvqMeXKZ5iHlB/ILbi6bzkjVf2QTOkoi1uTjFfIGNLf/GBpbs3CXCYEY/LXKZFxMp44GcdctrOhFVOufAZvrQqXCsXPbpxKG1AVR/sjAW2a8kqCfPxAV9Bk/CY+wwzWZPr1tDyOZAQ0j0ZmLgunyYgr9FhUbZML8/RZr+Kqv77lmQwZJ5PFAoBS19Mz80imrP4Rj2kuTaayIg7dMFnVSav9vMbmvX8mToav05Jp4tdUJaO5jEdJPOJb3VamNfld5+/zP2RJVAktWSw0s0VRyOQYjJPx2f/mCmtC/eDzLYHXoclDU1VGqhLEzu/iZEROxGeVxq+ExCjnIOjCZOMWMj7eZYrcXFazzZoYwpSfBfwzJyfTBiIRjXkQdbdTxximKS0IxQdktreSYyHgN1lY5jKr/bwJkFASj6CiNJoxZquBmcts4t8nHT0tFkT37xinybTFXCZ+V0eTCX8NSl1fIqmPkkxZqW80TUVad+JienaLAwB27nJM037emGxbBk2mrtG5llyTcX6Xl0ahSTRHvwVqCZe+RxQyUp7Gvs5p44YGthkoCpkuhUweMcQXVJbHA4+jgadpCutYBLHzJ1K8uUyIk/E1l7VNk0kJ5jL+79J4xCPkTAnxT6+I2lzfmMTSDzdlNI/4CZlUWkc0orrMINa95cQ/L2Rync8tH/DVZDhOpptEk1EVBb0qS/DuxzWBZp6G5iQUxUr3ryqKJ9WIYa/+nQlOEApRjXFfbRHa4gRHmkw2AmurLUhl3zORdFLfGIbJuB7S/nY1OYLBlVBW8iyZzGU8lyprC80PM84ehXLbZTxMqn/A4jz9zWUyTcb6/6SxQwLbDGTHy2aLopDJMVjH8hkfpE6X2RPsZ1/twLNvWhmnZcWpNFXxaDLiIE9ymoy4KmpJpLnoXqcj8lH62WgyIvHPl3KOxzSJ4wE8mgwNImpr7Y5m3DrnPbzz0ebAe4vBhoSWRBoxTnCQ6YavysmDF9rtLbJVCNB7OnjfPu7tLnOZV5NRVQW9u5dge30r3lzhX+iqpTWN0ngEqqpA01TPJEfeZ6QhikXvYlENiqIgorUtm4M4wTHvsixUGRIIMsGUoPxqmuoyl9GY4TlJWXlrHvyiiq/PcsnpByGiKS4hE8TJ0LtUOZfxuS9+ho/WbfM6VkSc5KO+5rIA4l9mMhZR1GS6EOjD+g0Q0mRoMPz6L4tx3zMfwTRNaXEqTVM9nIw4yBNJnXmXiYPsxv97Bz/9vRWsxQ8g3oTSViGTShuuv0vjERimW9DpwkTPR/yLA2NrBldbP05m564EohEVt1xyFABnwPgR/11Pk7He0zknDMOtl4x1tuuOuUymyQDARdNGAnD6nQw0CQOwXZjd74Qmzl7dLQ1RzM9Fk6Bljsr+fYqOJxQsm02cDGnLsmDQZEpHLGJpMpa5zAneBdz935VyRuifqqq4xh6ZCCOagpOOGoJYVENdY6vv+YBjLqOJ33Lptzb+++XP8dt73/YIaqoom0imfc1lck3GFjIqcO6kYdjHLnMhQ1HIdCGwbLU+++tt1Vy07bYk0u5EiPb+iISTkQVSxWOaHa3tvXOdINgAt198c6JtcTIi8S8LovO4MKsW8W+apidPVKbM1X5lo3fsakU0ouGgoX1x5MgqNmn5Ef8uTaadnMzHX27HlCufwc6GtqXYDwP6bpqqYOTQPljwx6koiVl1UWjCl3EyAFjOtkRAyW1eyGiq4jETOULGqqIo9j/XuW3QDEUNNd6GOBlW/dVHk7HKEVC6Gmu7I2TktXTSafe1VEVxaV1Re1ySsIlFNMFc5q9dULdU1eCIfwDoVelUr/QzlwVxMqqi4KyJ++PM4/bzHEMoCpkuhEy+/RQFnNYN/PWJlWx7XWPCpf0kAzgZ3lxGAXmUpDDIW4qfAHjvkqw0GSGtDN+5ZeSvH/H/4jtf44b73nFd20+IEPyEUF1Dgg2+spIIex4r4t97/N7VzoquvZrMs4stU+cn63e06zpBcISM0w/IKynIXGadY/WfhJCN+dnF63Dt7LcB2IsU0mQkHAEJ0J4kZITvRO9eU9U2vU9RQy2JZR/xT+sYmZCh57PaZ7Drksnarcl4M1oQNE1xJfCk/k5ms1hUdQU2BxH/Lk3GMAWvNvc5p40bijMn7IeTxg5h7/rTr3a4FmnBmox1L3Ee4ZFPIdNpEmTuLmDquu/4sD54Sjfw0jtfs631DUn06uasWBzvMi8nw3v30EqWiM0gspSfAN5eZdXdKY1rWZUhdpnLdHdGW+bGqhsAp9V4iX8T70r4l0ypLfyETGsyjVjUcl0tjUc4c5mc+P/+oQNRs6MJD73wabs5GSfDQ/7MbvTdPJkTDJNpKDIXZkI85k0Iet/TTnxTMmUgbpuoZNowacKkyYjmMnoHEU1pk2YofneZRtzYkkIqpTNBJ4ImbRknlEwZiEVVJFLWs1HmC9JkmlrlBdvEZ1EVxcVlUgCqI2TcqfWlLsykydjzvaoq0E3Tkw6JR2k8gvNPPMC+p3Xi7KdW45X3vvFtK3+dMEImbEmItqCoyeQYmYhPWoyKq8G6xlbXoKJVvYyT4TUZVrs85njP+EEmgAb165axhobrGnZnjmiq5xkY4W6Y+OCzLbj0jldR15CQxsnIWplRyNjPOv30g9hqF7CcGKIR6++ykihaWlM2xyWP+AeAfQf3AJDZJTUTVCZk2nWZQBicuYzd156cWEof28TUp4c3TiQeVX2dJlJpgxUeo3uIfaiuIYGIpqKbbZLz87DK1P/8IArAEkkw5hV/eh0/vvEl32vQkUHEf0RToOuOdxkJmZbWcMS/qiqu90iaDN2yrMS9Zg8i/kkwU+kL/p3eeL9bw9c44cDziV9w6XJE057VLjfxHwnIut7ShsqbYVEUMjkGy/Hko8rQB99mB8ideJ36VdoAACAASURBVNReAIC6xqSL+E8EaTIpr0ofjahQVTVYkzEMT9Guqt7lWeUtSunOABW5HCcgz8T19y1lUdiuypiKVS1TFvWfmZOx9o850FvtNGoPxDLb+SCR1O04GfnAam+RLYKTdTt/Uoa+cUTwoLNMpVZy1H336IFxhw3CbdPHes6PRyO+QqaxJclcfAG5JlPfmERlRcyJk+G+Ey/4KA4lW3g0mZg3GJMi0sUkoAz2oTJzcSLJmcsMg3lzkVBo8uNkpJpMGoP6VWDsQdU4/og97XZax4np9qVpZQznWoD1/kzTdB0rJlPl3zE/fss5Hk6WVV3UZHhz66xLv4/TxzvxMy0+/SMXKAqZHIM+rN+cQ5NezXZr0Bw8tC8Ay/vHXbHPqdESxMnQJEnCKJO5jNxDASsLbP/eZdiysyX05JBmpgbNw+WoPgF54TWZ4DbQZBSPap7zo7a5h2JvmhNpmILTget4SoPSXnMZyF1avj8X1R3TnPZIcDgZA9GIhpJYBFeecxgG9C73nB+Lqr4VGxubUxYxHqDJNCdSKC+Nsr7Lax4U0AhYwqF2RzM2bc1cXoCH11xmu+NzzSDtZs038kwZtKiTcjJpnWWKtlL9C95lXMnkxpYUy/ItageaapnLBvQux9X/Mxo97HislH0caZHknhxoLmPEv/W+g8Yf/935GjW8kJHdSxeEDC+gDhjSizlYABYnk6+FUlHI5BBbdjZj9rzVgcfQh6zdYWkP/XuXoTQeQUNTUiD++TgZUcjwqWKoI6khiH8TJXHHzDRi796o6l0OwzAzug8TaDDEYxGPiu1X512aIFPSnynHlB9I05GVlaUBRJNlMqX7epcBYNphMmXgiVfWtDkYLZMmkw15Xd+YkH4/R8gI5jKb+I9nqI8Tj2n+mkxzykP8ixN1c2saZfEIEzJ8ksj+nFDrURHHJ+t34Gd/eCWwPSL4TNLUXsAtoPessgrUfbtFLsDoUDknozPHGJ5k1zQVsYjq0sjnv/4Frv7bW9jVlPQxl6WZwKP/6bg+thfYgN5lru08/FyYg4QMb8mo7uO8b5cmEyJORlysMkGnuDN65xpFIZND3P3vFawT+c0t1MEpaWGPijjKbY8otwsz510mrMb5zkAdSVOVjMR/WjfYZAJYWkW/XtaAeHv1plCR/2ndgKJYdv6WpFzIBHmqEPEvm3wzebkl7Lo5oskPsNxHAUcAJVJkLpNfiwbcp1/twEMvfIoVa4LT/Pghk5AJG7XekkjjvOtfxP0LPvbsI1OKS5OxJ6dkyuGj/BCLah5TJE2QjS1JDydDbX76jXXYsqMZLa1plJVEmRB45f0NAICDhvbBr887jF2TVvbZgjQZytRAfZR/p9Re0UuOwfTXZBJJJ62MbhiuyTcW9WrkdI7cu0xn1oB4zP3ee9haHT1HOBdmLycjgudk+QUn5SsEgjM+O8S/kJ7KflflpZbm1ZyFA1A2KAqZHMLlhujDyZAgIW+OaERFaUkUzYmUQPzzucsETYYvt6yTg4ACzad0Ln9vcYImk8G/nv+EZS+WIZU2sL2+Bem0wUx4ojAhIcObH/hnAdwJMkVkEnLEHQQFWFJgIGkyvpyM3dYddr6z1jbapOn6fla3TAk4v9q8C2ndYMGSfNaDVFrHktWbmL08KuFkUrqXZxMRlwoZ67s32OayGOddZhgmtte34P5nP8LvH3gXzYkUSjlN5qN1ljnpwqkjXDxEj25tEzIJQcgQMc/3Zbq3H2/nR/xT7RTyvrTMZdY+TVUQj8mFjEy7IO8yEni8uQlwTFl7VXWHqio+wZhu4t/yEgyO1xI52f336Gk/q7+7NcBxMvbpoiZDb4oyeDfmSch0Ghfmq6++GkuWLEHPntYLnDRpEi655BIkk0mcccYZ7LjW1lZs2LABS5YsQY8ePVzXmDdvHm699VYMHDgQADBo0CD87W9/K9gz8CsvP03GyQhg/a2pCovt4Ccqck2NaIpnBZJMG1i07Gu8vOwb/Py0g9h1/IIxCbphegQWb3r64ts68RSGux77AItXbsSU7++NiGaZ8EQTExGLTYKw4CcG6vAyTSaTuk6R2zIQKR5j5jLD9i6TCxkacBQD0lYh41w/eFEhw/b6Fvzyztdw4pF7sfxSPGd227/ew3uf1LK4HpGT0Q0TpuldoYqIxzQk64QofU6TSaQMNmFaCxWDmWtbEmmkdQNlJRFPih7x3Xav8HejDkIqZSAWUa2MBnOWoco2wfGvjsaWn9mPupMo1NO6lUmDMkVb5jLbPKcqiEc16QStG4avuYw0mLhgth0zfAAu/9GhOGbUQDzz5pdSpxKPuUy1hGqgJiOM2ZsvOQq//dtbrkXerqYkfvL7hZh5ziiM3MdKP2TFqPEu5u7r0Bi0skU0ZRXKkA2yEjK1tbWora1F//790b9//5w35uKLL8Z5553n2haLxfDMM06hrjlz5mDp0qUeAUM46qijcM899+S8bWEQxvwuTjqapqK8JIqmFrcmQ9qKqipQFHdK8FTawNc1u7DmmzqHk1GI+PfvrGndcHmqAO5690E5jhavtLJHJ5K6rckorJMfe/hgjD2omt2bVkQ9usVR15BwEfqK6l4Nu9qXUcgYvhl6RXOZpcmY7H4iNCZkEuy52gKFCU35/iChTyvo5Z/V4geHWgsjWiUvXrkRK+xM3TU2f6dJiH8D3oWDiFjUy8kQj9PQlLJX+k5goWE4q+SIpmBXUxqlJRGXVti3ZykG9+/muibff9K6ERiXwYM0jSNHVmHBH6ey0gPuzBHW/36LAdPHXEZCJ6qprizMZEISTV6EVNrwugWbltCiTM8lwrmqqmDCmD0A+McMtYX4F8dsSSyC/r3LsZZzgvjg8y3YVteCp15d6wgZIUYtImq89uNV5FmTCdULNm3ahHPOOQfjx4/Hz372M4wfPx7nnHMONm4MVwckl5g3bx5OP/30gt+3LTAMEw+98IkrOaE4CDRVQWlJBE12bAeBTEw0UPmOlkrraGlNwzCctOWaRsR/sLmMJoJS2wGA1wxEtVwGR8g4earGHzYIYw4cwLiBBtvN9Ajb1dhtLvO/dqZaHQme5BakDDOXRd3mMn9Nxtq+044RyuR04IegdCZB2wHHZNqS0NkAJ01m1sPvs/fb3Jq2kldKgjF13cxYb0hmLqN+Q1qnm/h3gmwVxVpMlMWjLiHzown7ezz3+E+SjdDmzXXUBut6nJARNJkVn29xuTPToYZpIpXWcfMD72L9pnpuUnc4S8Mw2bsUtRGCmGHc2mbdm76RrKwAIaKpgeYyekb6jsHmMu/3jUc1l1BYZ1sh9hzQnW0Ts234m8ssDbRDhcxVV12FAw88EO+//z6WLl2K9957DyNGjMDVV1+d08Y8+OCDmDJlCqZPn45169Z59n/44YfYunUrxo8f73uNZcuWYerUqTj33HPx+uuv57R9meA2l5mo2dGEJ15ZizseWc4GrUeTURWUxWXEvxOMKSKZMtDUmoJhOrZYmoSCJjVa2dxz5Tj84+oJANzmsjDZWpNp3QoQdQWIkRZhr46FrL38hBN0j8yajM7cW0XERHNZ2ggk/sm0RwPrvY9rMfXXz3ryqWUCXd+v7UFCnzTBlkSalUAuiWtSJwJxgqD0L2nDgJrJXBbVPG7CZJ4hHkwk/ul5qH+VlURcga2lce/kTDFfQObA2n+//Dl3rOHqhw7P5R5PgLUYaE2m8f/+uRQ/l3ixGbqJz7/eiXc/rsG9T65yxYpENKcypkyTceW0S3vNZTQmS3zMZTyse8lcmN3PSN8x2Fzm/b5xwWGBNLye3R1ejH9O2XXonXazx2lTln0/LEKZyz7++GM88MADiEYttaq8vBy/+tWvcMQRR4S+0amnnopNmzZJ9y1ZsgQzZsxA3759oaoqnn76aVx44YVYtGgRNM35kE899RROOeUU1g4R48aNw0knnYSSkhJ88sknuOiii/DQQw9hn332Cd3OXEE3TNdKK5XWocUiHi5CVRUrSl0g/lOCWyePZFpnHcxVEoAj/i1XYfd5VBNkCJe7S5YiPwhLP9yMfr3KXFqPQ7q7NRkmZATi3w8ZS9sm3SteHhGpC7O/uUwccJ/bpoe1G+owav9+ge3gQULTbyUaZL4kF/C0brg0GRmPExXaS/yCoZse70MRMhdmR8hYbXDlLrMdCgBHWJQJ5jLZKr5bWQxXnHUo/vzvFRkDa+e++Bn7baUF4hY7lDmCew2Ow4zOMlQ0NCfR0JxEt7KYy1xGxet6V5Zyk7ojQHmujs+QEIs6waSptOHhd+iZ/MxlPPzMZaafucz+Hmcfvz8eW/i56xxNoqn6mfn4viMGI3s4GftYyuTQmEVdqWwQSsgccsghWL16NQ47zHFX/Oijj3DooYeGvtH8+fMD9/Mcz7Rp03DbbbehpqaGkfiJRALPP/885s6d63uNXr16sd/Dhw/HqFGjsHr16oIJGX5qEIVMOm3AiJiuiV+z+ZaykghaErpn5RPRFC43lrN9V2OSTVB8jjMydYjHEwzDhCqklojygzukDX1wvwpBk1Fd/+8ShAwfCBg0H2YKCKVsujKIbUimdBiBcTLyZ806eNK+/AMLPsYBQ3ph2J69XLuDNEueuKUSwLGot54L4LWnE/GfNoxQnIxum2TEVPHUj0RNhlIGkQNKWTzqepelMR+NknMhD4tEUnctdphziEuTcY7lK1kmkjq6lTkCSTcMTsiUOOZkRUFlRRz1jQm02OZHABjcz+GVeHdmmbmMBHV5idyFmUdEkv3g2tlvMy9CFvHPzGVWO8ceVO0RMn6ajAye5LRCRgZpWyMqYlGNadO5hq+Qufvuu9nvwYMH4+KLL8a4ceMwYMAA1NTU4I033sDkyZNz1hByKACAxYsXQ1VVl+BZuHAh9txzT+y3n3+6av4aGzduxMqVK3HJJZfkrI0Zwa+8dBO7uHrfybSBEmHyIM2BXB9Fm6jqWsE459buaGa2dBbIxkX8+5brNb0R8K60ICHMZYC12nphyVfs76hgqtrFzGV2/ZEcaTLJtM5ISvEJabUX58xlZoC5LObj9ptN8CTAZAwA4OEXPsUtl7jTugS5MPN1VKiYnW6YUsHkMZdxnIyfdkdg2Q3SjpChCZAEHX1DlknAXhiw3GglEdd3LPXhI+IsniW8kBE1GVnSUcbJpHTmdg7wkyqnyeyyAot7dIu7OJCRQ/vgyVfX4sN121i/550X+D6RSuvSfGCAM16DHBtkKXZWf7GNe0awdhmmoznK3NFlwoEyXPTvVYbt9a3sXkEZ0EVLBR2qKgoqSqOF9y6rqalx/X388ccDAHbs2IFYLIaJEycikfAvhJQtrrrqKmzfvh2KoqCiogKzZ89GJOI0z4/wv/baa3HsscfiuOOOw9y5c/HKK68wE9vMmTMxfPjwnLUxE/jYmLRhCOYyw8vHUL4tyqEkfGR+BcPPfbU7mpwVF5/jTLWKKvlGnwekWQEQuM/Vbju7AIHMZDRAiNfobwd6HrBXb3ZskJAhAenXDj7Hlgh6Vy7vMiNYkymXDCxZTrUg8EfLVrbuFO5u8wWfMWEbVz5Y9vl8ORndYKl0/ECmzbQrbRFpKm4HEyeTgOE6rjQecS0CSiScDADEI877D4vWpO6KsZFlVCYh8+XGetw59322XdTceXMZf56iKBg+pBdUVUHN9mZ2P8okAMAV1JrSvZwMgcZrUF+OaqqvkOKf0TGXub8DD5kZm2LRjj9iT/x3yXpss5/Z/c6CTeB8zM6IfXqjqo83JVEu4Ns7b7vttrzc0A9z5swJ3P/ggw9Kt99yyy3s98yZMzFz5sxcNisr8JODrpuu2uHJlC4l/QHH9CDGl/AdhM7s2S2O2h0tbPAwBwFVtRMApn1X42IpZBF+kzuf7ZWO4803oiZDnEz/XmW49zfHsjQbQLC5DLBW2DFVPoHx6U+8bXebyzJF/ANWEJooZLLVZPhvKmubLg56rj28uWxDrZVMlFxsCZUVMdQ3JqUaaFo3QnmXkZaXTOk465aXcfbx+7N2kYcbCWnynKoTirCVlUSYazEQQpPJ2lzGazLW/644GW6+N4RxBnDeZbrJItcN0wm8VFUFJbEIenWLY1t9KxsH/XuV4fZLj8bAvhWsvg7grvp6zQWjceuc99i+8hI5J8xD05TAvHjuYEynZIPHzRhyTYY3CXYrjzEhIy5qZF3j6IOr7f3UFuDX5x2e8ZnaitBxMl999RWee+45bNmyBf369cPkyZOx11575a1hXR2Gh/g3PBOYxlbfVk/wBDfyncs+t7pvBUvgR9ela9Eq1I8HyDTp+q16Zvz5Dc9xLk4mSu7Qbo+taET1xFIErf4AW8j4CJJEgJChtiuKgljEKkPgV37ZOcc7ArPNl8nzaDJNxhDMF/w75s1llGVY7Cfdy+Oob0x6zG6qqsBIESfjfsZ7rhznWvCQANle34KmlhT+7xmnlgx5JdH3pBIIvGkHsExEvBNFiQ8nQ+8gSJNZ/cVW19+Wucz5FoqiWNm6JeYyEU5CWsdcRgsNQ3fSF1HTe1WWYFt9q+udDR9iadp8fyAho6kKjhxZjaMPrsZbdg2mMqEK6d4DvWWNI5oa6C3Jm8uSaQN/t3MehtVkDjugH95Y8S0OGNILr7y3gW3n+4loLgOAebdPYdcjy0tIK3mbEYrpffXVV3Haaadh/fr1qKysxPr163H66afjlVeyS4S3u8NN/IvmMl0SI2PzCPbAFAPNeK8hKhgl1qwg332V4gB8zC2AnJNxtSdEnAzguEsTGOluC4CWRNrltOA6N8MtgniZZADxz7c9ZrvsBkX8+yFb4p/3HpNqMrr/RCmr4aELmgzlAxOz7LIFhSTocUh1pWvio8UKb0YiUC4wWkHvv0dPqKqCVWtFIRNxvUs/zypG/PtwMjXbm3Dt7CWuba0SM6iiuCt08r+vuWAMrjxnFAC+tAbsvx0hrZsOP0n9ntLgyPoF7wpuCRmTvRd+3PBa3BO3now7L/uB51rRSHDZDd5cJp4XBuNGDcJTf5iM6j4VrnNcWp7E9GyVBLG2dbfjY/xKd+cKoTSZu+66C/feey++973vsW3vvvsufv/73+O4447LW+O6HLiBkNZNbNrWiNK4hpaEbsVteDgZN48g5gLjvb1+eeahuP6+pRg6qAfe+6SWbSezhEP8e+8DWJNnRk7GZ0Lee2AlvtxY77RbVVwdm4hl+t80/T1Z/FyKCX5CxjQtkwK9K1GQ8iYjwzTx3NvrURrXXMFpfuBLNmcqny2Cn0jEXFbWfi5jNlcxFJAnEk3r7uShlRWUNt6bR8viZMyMiwOmydR5M22TMKD3VxKPoG+PUqZZEazcZc7fft83zrzL5N9Rnowy7REyfIYLwK3VVPUpx5adVvvY+yVzGef4YhimQ/zbjafFmmwcuAOeLU2GFnp0fGk84jrOLyBTU5VA5wfeXMYjbJYExU7uybcNcPe3TIvK08bvi+4VcRx7+B6h7tlWhHqimpoaHH6422Z32GGHeZwDinDQ3JrCt1sasb/t0iol/lW3kPG4LnIdZNSwfpg/awoOGtrHdUwq5ZjLSmKWK7SM+DfsVV2QB5mfuSyZ0t2lf+2YHMCawFRuIIolaUVkMpd9un6HZ4ID7MnXMP05GW6ipYmsJaEHDjJCXy5WIntNJjtOhofIW5TGI/hw3Tas+9YR6JVMkxEyAqvkXeZNFSSCvtU2iSZDbeKrJoraolVVUs347ehYwD+DguwShgmPh5yYSJX/LgN6lbkK5AHuejIkpPm0/oogZGSkvphVI502HE3GPr88g5MFIRKRR/wTaE0k9s9Meeik9+LOWbxiI6u5IzOX8YhGVJx45F6hHX7ailBCZtiwYXjggQdc2x588EEccMABeWlUVwU/h7QmrbQm++9pJfxM2eYbHqLbrQhxhRrRVM/KiSf+Kyvi2NWYkKrpLAgtoENtqG3AlCufwUoh7X1rUkcZd19NVVnHFjsxeej4TXyZ+vOsR97Hhbe87NlONn5nxSsX2N77ZR5AFPEMZC9k+ONlrsSiSykPcTFAWsuN/+eU3/UrgEUrfd0OsA0C7adqrEHHAN7+SCbaMHMRvQO/Vbzf+xXvqaniqhw45tBBePqOU1DCaRMi8c+78BumN40LCZn6Bq9nrIyTEdM6iXyMHyi7AEH81nyCTB5hBLmn3dy329mQwJV3vwkgszdpoRBKyNxwww148skncfTRR+OMM87A0Ucfjccffxw33HBDnpvXtSAj+ohUTNmeQICzUiQh4k9mez9PWVzOyWiqgsryGJJpQ2qGCWMua7I1gKUfbnZtTyR1l5uspjnEv2j+chIt+pjLQg6ixxetwUauwqJTFdMnoMzPPBdwuwunjkDPbnFU96lg27L1LuM5F7kjQYCQgTutT2W5N1U+2f9lGYGZuSyTJsPMZV5NhsC/P9F0RW0I8+3oOn7CxG91L9bEKS+NuYIDDcOEojqTPb1rkfgXzWV8LAjgCHJZxm+puYxz7Qa8488PYjCm+D4ylYjIBn7ehZkWlYVCxjdmGAa2bNmC+fPn49NPP2XeZQcffLBvepfvKmR8ArnvUup5wE5YmNQ95jIRMtVZ1GRSXDAmDaBX39/gOU+3B1yYlT3vOXTvk6vQ0JxEr+6Ol5iV8dmbuBPgNBkftV/W5y84eTjqm5KY//oXbNvD//0Uq7/Yipt/bgU3kmnJj/jnB9PNPzsK1/3DIpeDJsbDD+iPh26Y5PK2CltkzDnef7UKCN4+wn7TMFESc/KK8RoVQVYlErACZ3XdSlsfVpPZHqDJ8N9LfMeOJpO577AYF5/X6Me5iYuHyoqYkABTCCyk2B/7/bqJf9X5zYh/uq5/zRsp8U9CRgkeqyIidqlngtiv6FHI8WLooErsM0ieWT4Tpo3bB+9/WoPWpO7RnLN1fMkHMmoyqqpi+vTpKC8vx+GHH46TTjoJhx9+eFHASCCu0g4b1o/5//OcTAnTZCi+RP4ZZCtj0asnwQVjdrcHkMjtAM4KL0yf4+/x36VfAXDXFte4GjfioCM35kyczJ4DHKF1+rH7YtT+fT3H8nmlaCImISbO5/z9hnCeVWEGGX9upiSdItyci9xMyfZ7zGXuRYPoOQiA1ZIR4dJkMggZej4xowT/3IHmMrsCI3O7DXilLMbFT5PxcQgQ+1FleRx1jY5JS1wgeTgZMpfpoibjJv67SwS5eE3A5mR0wzEL2/vCen+JmowoZOh6ZHU4bvQeuPSMQ0JdW8TQQT3w71tOdo0XIHNcXKEQ6o2NHj0aK1euzHdbujz4Vdo/fzsBvzn/cNYpeRdm8kKizx+WkwG88QmM+LfNZX4g106Z+nzXjGNcWXVl2oLLXMbFyYjpWZwcWMHmMlHDkJUQ7tmthP2mVaHfIHdPmM7vMGOMfyeZ8qeJkOXX4hEoZGCiNCD/1ZXnjPKNwmacDDcR+oG+lVh51C8Dsfj9RXNZUM4uRVHs5Kw+QiYt52rE719ZEcMuXsgICyTRXMaXXybl0jCd/WTWDdJkRHNZiif+2yBk9EBNxroehS0EJdsMC3FsGz7BmIVGKANjdXU1LrroIhx33HEYMGCAa4K4/PLL89a4rgZeyNDkQAO7vjGJOptsZCYQe2D4rURlE7XYkSjHlGUu8x9AQZzM0EE9cNRB1Syoi4QgP1Hwtmjei0xcgdIgzGQu87pueo/nJ/xUQNoNcTs/EYSxSWvtEDJihHXQfm9pYPeiwVtT3uvoQWC5ywzTV6A71yHTkvv+fLr4IE2GcYgqcYjB0wa5V8vgV/3Uay6Lo140l3HfiZ6JzJX0akXvMtGFOWgy58chpZURzWWyxZD8Wu7yy55gWvtRKONCUG2asPDmJusinAxgZUCeMMGqP1JbW5vh6O8uZPZm6pT/fvlzVkODBrGfSSEaUZFKeyO5pfdkLsxqoCmAFWvyLeLlDDAaiPyk5DKXqQpn6vO6u9IxMjh1NNzbZYOXf59Mk/ERMq4JiLt4GLK6XeYy3WCxULLPaRgBnIzpTiMi9h/Vzl4gbbOmsAk7rCYDOFmWAVGT4TgZ0dNLI+3T+juWYdWtKIq/uczn/Yr9qHt5DImkjtZEGiXxiCewVhXMZcTKGFwwpsFpNaqPBu1qA/8tUnLiv63mMj/ivzXhLoTG497fHBuaA+LbyN+zM5jLQgmZq666yrfccREWTNNJcsfDinx3m1JKfMhc5xxbyIRYhdBqSVUURAI6JNmn/VY2/EREA4A3bfB8gaqqvuYypsn4rK75wX7XFcew+AbZROkSMjShhjCX8QXcsjWXZarOKUI3TBwwpDc++GyL9Hu6Iv6F/WKaH1HAqarzLfbbwz3+VEVxPAtDcjKAZfoiboYXJkHmMvJeYuayDBOfqiq+WSfCChnKdFDflLSEjCEuJOQuzIbhvGfD5DiZELKBb0MybZXeYHV27FuHFTLRiNuF2Y/4J0EkywXXq3sJyrOIxpfVj+r0mszKlStx6aWXYvv27aiqqsLf/va3YmyMD9Z9Wy9dySqKgqimuswEtGrxMylEIypaEuGif8V6MmKkNCGTCzN/LzIx8BMCP/GoijfrsXgdPy1MoSA0RcHQwc7EKdNkXOYyIRW6+ITiRBuJqNCTejiPKJe5LPtgzIiqenJt8fsJsu/Ct08UcLTv/msnejzPVFVhmZIzLUb4b1tW4ggZ/ttpAeYy+pb0fJn4A1Xx79t+nIzo/EIcIBHjYtkGWsRI08pIiH9eg7nx4iOlixqXkEnpSOkGm+Sz1WQ01SpPTvnzPMS/3Z5fnnkIFiz+EsP26uW5RrZKCN//vtxYj9VfbMPwId7rFhqBb+z222/H1KlTsWDBApxwwgm4/fbbC9WuLoVN2xo9SSR5RH1s3EGaDBAul1gypUNRnEHgJ5gyuTC7ywpY7fJT960Ehhk4mQzmMrEZssHLC7kUMw1l1mT448IMVF7ragvxr9l52qTeZQEuzDyZPXxIL6+5U1eaUwAAIABJREFUzH6mfr3KPCtdlTN7Zeon/H7e7En9UFXc789v4ZDJjZxvm7+QCafJMCGiE+cir41isFT/HPHvcgJwB2MCwKj9++GgoV5vRl4rT6YMpDlrQracDGVQoG8kVkilcTCgdzkumjZSOl6yNXXxr5zKIWze1pTVNfKBQE1m3bp1eOSRR6BpGmbMmIHx48cXql1dCqKwmDjGnQsoFlHBf2qHk5FfL5PJ6ZEbJ+Gb2gZcc+/bSApmNb6v8mV3M7kw8ytZmheDklX6FVmKMgHpZy6z/vd6l3mP5yf8tM/9COJEGxUI2yC0x7tMNwyoqiVkMnmXeYl/EwoUzLt9MlRFwZX3vOnaH8Qf8M8VNk4GcJs9aWIXzxffJf1NfSmTuUzGyWza1oh1G+pdVVJ5xCKiYHNP0v7Ev+DCbATnLguCaC5L617vsrBpX8jESIXixKq3YaxYmfL8eeHcg5x3miWB2YVGYO9Mp9OsAFgsFkMqlZ/KaV0dfH2J3/7PaFz2I3dZ6ooyt6lD9C4TkclDq7Iijp520aVUSndV0OTH0vknHoAzjtsXQOa0MkHmsu7lMYw9qNp1vBOBL0wOITUZsR1lkhodgZqMT4oe53kyE73Oue0h/q2Iez9zWTqAkzFhfa9oRLMqKfpoMpnanNG7TOWFDKfJkJOGIGTEWJaIYJqqKPV3MAGsCV18FT+77RXMeuT9AE1GFHT2JM0qPrq/pUj80/1SaYNtc9WTCdEPoi5NxhIyoqNJ2ASWNA6o/X7EfxCyziDO3YJqVGVToTRfCNRkkskkfvOb37C/m5ubXX8DwKxZs/LTsi4EPp+RzBWxW5l7ApUJmat/PBp/eOg91zWCbO2sEFXagLvfO+fousFqzmfmZPzNZb/44cEecwZl2fXlZDLkEgtjLkunvZpMaHNZJLy5rH2ajCVkFFWRcnKu/FsyTYbnZIQJOCiZKd/mzN5lvLnM6Z/UD8V3KtaCocXO6AP64/TxQ3H6sfsG3k9VwwVj/vLMQ/CXx634O28/Eol907X6d8xponeZyYrmuYIxQ8gGfsGUSFncjliuOowzDuAkt6VFhh/xH4RsFRl+keNXVK4jENiSn//854F/F2GBt+XKchuJH5yIf16FHnuwoylUhKkhrpIHmOGrySSSThZiqtLnN3G5VtzcqhCwBICoVe1rp8A44sABru0sC3OGXGJhVmk8Ec63BZAR/4KJR6iUGQR3nIyJ+sYESuORUO6jFKcSRpORxcnwr+GCyQfi1jnL2N9KQNPdpqNMcTLBmow4AYsOCBHOBHrB5AMD7wV442R4Xoo3l/HjRjSX0fdjaWNEc5lEk+lWFkVDc4o52fD8TBjNgedOUykdJpzFiozbCYKoyfCLDUUJ155sk2Xy3S+sg0IhEChkLr300kK1o0uD7wyyFYRXyFBqFPlqT/RokYEm1WRKd7k5ulbGusGuwec4k+HLjU6JZdFcFo2oHqEwdHAPPPmHyR5zWaYszH51NGTgPZGYJuPrwuzeTs8QZkXHtzWZ0nHe9S/iyJFVuOaCMRnPNezKlG0h/kVN5siRVZjy/b2xYPGXAILfkZuTCa/J8Knq/biVU8cNxY5drfi2thGff7MzdDE7gsjJbOXq2PDmG16Ii5OiyMlYfGIw8d+zeyka+KSakqJlQYgJ5jJFUZhGwpwsQobQixrQWys3sX1hhUe27sf8fCJLkttR6DzibjdBGCHDiP8MQia49otjJ+cnSfrVrSyG08YNZdd4zU6a6ddxJ4x2nBUMJmScfGGy82STlKPJ+AkZ9/9BSKdN7ndw4KEo1Gg1HiZrLv9sX26yarks/zRc0DFVHwxD/PtxMjzEeB8/8BNK5oh/Zz/fF8lcpsB9n25lMVxx1ijHnJZlbhJLq3P+5s2AYYWMyMl4cpeJxD/AeEoCT/yHMXPFBHMZT/yH9eSTtX9DbQPmcclfMzVlr6rMhfZk4HtXQ7NlMrz6x6PbdK1cotMImYcffhiTJk3ClClTMHXqVLa9paUFV1xxBSZOnIhJkybhtdde873G448/jokTJ2LChAm46aabXNHWhUKpJMnh+MMGu/7O5MJMdvOgwEC+s7uEjP1zxtmHoqIsxjLLvrzsGwD+q+MjRlThsZtPsttlbXOZy7I0E/jdhyafMJ4zKV3nfttt8eNkhMFPbZd9D8+5XFu27rRW3fvu0TPjeQBYqn1VkX/PoKhvU5LAMKyQ4bWDTM4KfPG7Uol3mR/oW2Uyx4kQXZh5QduSTKOsJIJrfzLGJVhE0zD9zSe8lHEyaS4Ys0eFV8hQXw5VcI1rT1o3kEwbHo0kEnIcRDWnfWLOuExtuXX6WNxx2fdD3YcHL9gbmpM44sABLjN8R6FTCJmFCxfixRdfxJNPPokFCxbg/vvvZ/vuv/9+VFRU4OWXX8bf//53XHfddWhq8vp+b9iwAX/961/xn//8BwsXLsTXX3+NZ599tpCPAUCeHmLk0D646eIjPcf4CRmquS1WTuThPxlZv/3iVYLdYq3/peayLAeX332ycSkVNRlVCZ/njdou+x6ZzgWA3pUlkiO9MGwXZr/YkKAszbLj+ecLekd8/ENjS9L3OMDdP8olnAx8bkPty7Zao2g65E2GiaSOfj3L8L0RVdI0MQTqt2nd8BQeo9+KwnMdJioFTYbnZMJ0X1Ho8sQ/E3QhBS5fikBc62YSMt3KYsxhJxvw2m3N9uZOQ/53CiHzwAMP4NJLL0VFhVU8qk8fp8Twf//7X/zoRz8CAOy1114YMWIE3nzzTc81XnrpJUyYMAG9evWCqqo444wz8MILLxTmATj4EW58B87kwkzmMtHLh4dfri76SdyIOHiDhAUNelHIRDQ1a1u037MxTSbEoBc5GbebtftYj7mMNJkszWUEMa7BD4ZpvX8/c1lQunfZvfmVcpCQoWwJp48fiuM4U6cM/KTGZ7YOXxsle03G5CZWlyaTSLMxEoZztLKHW9vEyZlKUAP0HRS2QAOs/kM1irIpHc2jwvYMpf4QVpPhNSBeIwey9xoLC5Hj7SzkfyhR9+STT0q3x2IxDBgwAIcccghisWDf+SCsW7cOq1atwt13341kMomzzjoLZ555JgBg06ZNGDhwIDu2qqoKNTU1nmts3rwZ1dWOalhdXY3Nmzd7juso8FHS9NvPGkbmsqRP7Q1AFCw8JxOsyQTJCjJhybzLQmsy5P3lI2TE+h489q6uZJwI4PUu40n/g4b2weovtrG/xfZRHrkw5jLZs4V1ZTYNy7XWN61MhtxlnrZwWkPQO//J5AMx9Qf7oH+vslDtJPAaWl+7/kidpBQx395sNRkxrQz/3M2tKfTqbt03aN6PcC7KjoeYcB9VdeUuUxTFirexLYlrvnGcWcJxMt7BMaiftfAljSksJxPlzH2tQqxKW0osh4HYnXbs8q+EWkiEEjLPPPMMVqxYgT59+mDAgAGoqanBtm3bMGLECGzcuBEAcO+992LkyJHS80899VRs2rRJum/JkiXQdR2bN2/Go48+ip07d+Lss8/GkCFDMHp0x5NWYXHXjGPwbW2D736eJM+UhZmidf3yPAFCMB7f8e2fUR9uJDD2QjSXcVH2YVdfESZk5PtZfQ/J9W68+Eg8sOAjvLb8W/SpLGEeMotXbMSztscV4dqfjMGWnS345Z1yjo5ebbbeZYSwiTINk2qoyHPGBXIypvf7RHwWDyKiETVrAQMAPTiT0sH7eVOruNtHZHfuOJnm1jSq+si1bB7M3GSYMJlnl1eTYdc2TSgBbQ2zSJJpbIP7WcX1SJipITV61v60gVbB0yt/moz77y07m/NzoywRSsgMHToUEydOxI9//GO27ZFHHsGXX36Jxx57DLNnz8bNN9+M//znP9Lz58+fH3j96upqTJ48Gaqqonfv3jjqqKOwevVqjB49GtXV1di4cSN69bJslJs3b8YRRxzhuUZVVZVLkG3atAlVVVVhHi8nGDqoB4YGlE/lVXHiCU48ai/psRStG6TJqEQ2m5B6l5GQkeW88gOrO07BmLy5LGykc4Ya7465zNuOHt3imHnOYTh13FC8vvxbzHv9C+xsaMUbK771HFtWEsVeVZkz1LbVXBY28p8SN/qZy/j3oBsm/vrESpSVRPHTKQdak7joXebKhh2qCVlBrBvzk8kHoiQuN5vR82TrXSYKXP53U2uaufAHmQMd4t/wjXWxhIztwgzrffm1NdvMDwSqNqn7CDrf9lOcjGGgJVEgTUaIHvvxScPzcp9sEar3PPfcczjvvPNc284++2wsWLAAiqLgwgsvxBdffOFzdmZMnjwZixcvBmBlFVi+fDmGDRsGAJg0aRITXl999RU+/PBDfP/7Xs+LE044AYsWLcKOHTtgGAaeeOIJnHjiiW1uU67BazKaZuWruvCUEfJj7UEYRPwDzqrKZS4TEvlV963ADRd9jzsns5DhU3RY1/LGyfiBJgdfTUZC4ooYUl3JhOTP//AKupW13RQbxoVZNnGENpfZiRtFExF/HXp1umHipXe+ZjyBWLdebEs+aoGIz3ra+KE46agh0mOdonrZmssUl+mQD0RMpnS2yAp6PI3zzvLlZDQFfG4zRVF8zcFh3qUnh5vt0ME/Q/iIfyd3GRUmIxTCXDb56CH43ojCLbKDEErI9O7dG6+++qpr2+uvv860i0QigUik7Z4MF1xwATZv3oyTTz4ZZ5xxBqZMmYKxY8cCAP73f/8Xu3btwsSJE/Gzn/0MN910E3MQuPvuu/HYY48BAAYPHozp06fjzDPPxPHHH49BgwbhlFNOaXObco3yUnf5Yr/YE8CqIwEA+wyU13dn17EHf0QS8c8PqsOG9WdmkuAAP+t/WnkSYRnUVhHRjMR/OO8yOr+5NR1YjC0TwlQcbA8nw5vL/FL9kxbb2Oz2AhMj/gE3/xF2QssG2QgMep6siX9FcXlUiQ4PoTQZmtxd3mXuY3jin96l3wSebT0ZADiAS5O/n+3SHtZE6UT8m15zWZ74eL7/7dG/W35u0gaEkgzXXXcdLr/8cuy7776oqqrC5s2bsXbtWtx9990AgFWrVuH8889vcyNKSkpwxx13SPeVlZXhnnvuke4TSz+fddZZOOuss9rcjnyCTxGeaYLt17MUd11xDPYYENxRWDlczqmgZ/cSbK9v9XTkMJUBRXNZKkMApAyRjMQ/3Sv4Opu2Oi667REyYSZIqSaT9lHFODgC0zuxsuvoBmIRKxv2V5t3Ced7AyHVkJxMWzBynz5ZaUf0rbLWZFT4cjIAV2IgkJNxzE1OnIz3XTHi397mK2RCPHefHqW49IyDUd2nAtfMfhtnTdif7Tt9/L743ogqDA45edOY+cND73m8vPKtyZx/4gE44Xt75eUebUEoIXP00Ufj5ZdfxptvvoktW7bgmGOOwTHHHIOePXuy/UcffXReG7o7IdPkoarugl5+iEU0NCPt4h2u+8kYvPdJLXpXlrqvSRpOiHubpjUxrPh8C7qVRbMaFDS4/KbosJoMXx+nLfXPf/HDg/Hmio2hjuU99Y45dBA2bm1gCUCDwASmStVP5d5l8aiKBgDfbmkE4EyyJkxPfjJeoOdyMnrmjlPsa2ZxUns4GVecjKDJxCPsOD/wlS/9TKw8JwPbXJYpnVEm0OT87J2neLI+hxUwgDs+y1tWO/RlsgL1v3GHDeoUFTEJoXtPr169MGbMGIwePRpjxoxhAqaI7JHJDBJ2QBBhy2syvStLMenIvTzHUqfLKGTsybJ2exPWfFOHMyfsF6otBJqw/Yl/f+8yHj871fJUHNi33J/gCcCkI/fCrdPHhjqWn0N/dd5hGNi3WyhzGf8sfsGYad1gZpiWVstsQskgDS/vHzoYM1tQwGg2gqtdnExAEGoJVyzN9xq2Y4sVjGltkxP/TpyMovi/s2wn3fYK+CCHk3xpMvTKszVv5huhlohbtmzBzJkzsXLlSvTo0QN1dXU4+OCD8ac//Qn9+/fPdxt3G1T3KcembU0562TUkcNEtdMgC3JhBhzPIHLhJe+a0BDcoEV8b0QVRu6zAeecMCzwMpUVcRxz6CCs+WanNIV+LuGpRRNRshIyqhKcu4wJGZsAZpO2kCDTagu/eg79CHlBmzkZ1f0uDEGTiccyazKAJXD90spY+91ljRUovpmrC72yD9K+8yVkSPXMB5fXHoTqPTfccAOGDRuGZcuW4a233sKyZctwwAEH4Prrr893+3Yr3Dp9LC4942BX1mQe91w5Dj+dkjmVOsERMpkjt/2KhcmOM03HxBE20p/gxNrI95eVRHHr9LEY0Ls847ViURWJlM4mu9+cd3hWbQkLcaUekRQQk4H3evLzLtN1gwX5JUjIcEGvQcR/PrzLskFbORlFETkZ97uk/pppMozYQsQvgFdTVVcSzEDiv8CvMujZ8h0n0yU1meXLl+Puu+9GNGpNjmVlZfjNb34jdSUuwh+9K0sDCbkh1ZUYUh3sUcaDVkuZaq4DzgDNJDNossw2wpmdr7rdoNuDeFRDKq2zyW7UsH6eY26/9GjUN8oj1sNCnLyimhpOk+FW2H7eZWnDZJMqxUto7B3JXJjzR/xni/ZoMkHEP72PjJqMqlpxMiyAVyT+Fei66ZjT4K+pd7TA5pFvc1mX1GQqKyuxbt0617Yvv/wS3bu3LSV1EbkBuQuHSgIZshwxkbZOrqbsSV/A34U5G0SjGhIpI5DHGT6kN44c2b5Ms578YZFwQoYPEpSVHAZIk7HjnihegotHksV++LWr0MgmTT4PVQjG9HqXZY6TAWyN0nCEiOc7aQrShuF4ltkOGFYb3NcKk/W7UMiXwBt/2CAA/jWXOgqhNJkLL7wQF1xwAX74wx+iuroamzZtwrx58zwuxEUUFtRXw5jL1JDmMov4z77cLGuT/b8fJ5MNYlEVSc5clq8VoKd0s6YiFcqF2fpfUSwuQE78myyFPM21TmyHGVxPptOYy7KPk3FxMn5xMhn6lqYp7jgZz7tSYeicuQxOH4lENFeC2Y5+lzzy1ZRLTjsIF0w+sGuay84880wMHjwYzz33HD7//HP069cPf/zjH3HkkUdmPrmIvIEGVDwM8U9CJoTrsGmYWRdpIlBMSzbunn6gLAnkTpyvweldIassxXyQYOMnP1/iXzdcMVIAJ2Qg02Tym1YmG4T1BBShKN50OjxI887UFzX7O+hB5jJO04HifMuopiCZch/bWZC3xZKmoqK0cwkYIKSQAYAjjzzSJVRSqRTOPfdczJ07Ny8NKyIzqK+G4mRU+j9Lc1mWq6I9BnTHLZcc1aZ6GCJEM1O+VqMy7zLA0kKiEf978pOfqsjdtnXDhKYpbndbXpMRjg+bILMQoMfJ9r17ORm36ZEcITKayxjn4h8nY2ncpMkorK2iyaijZczB+/bB4P7d8Nxb6zvca7DQaHMuGNM08cEHH+SyLUVkCeYxFmIAhXVhJlMHTQz8wL7mgtHo2zNzWo2DhgZn9w0LMjNRyd58rQDFQe9UNTQCa3IwrsCOz/DzLouoqkvIOPm2JN5lnFDraAK3rWZKMRhTFL4xodaR33NqmmpF/PsIO01VkEhxxL/ivE9xcZQ/t+FwUBVHAGbrsdnV0TlKpxXRJjj8R4hjQ7swW9xCWqLJtJdgzxakyVA9jnzNuR5NRii56wd+hR3kXaZpimV2tHl/Kgsu8y7jnTg6mkfoU1mKrTtbsi5+palC0TIhTiYadZeh8OuTEU3UZIT7aKrLxVnhJvLOxkvwgbAdraEWGkUh04XBsiaHONbJXZb5mrwm05GraWYuIwI3b7Zsr3cZkDndv2tyU/05mYim2jnJdNd5hglPyH8ZV2Sto1ff1/5kDFau2coStoaFGCcjanjEtWXUZGxzmJ8Ls6YqVqAn58LMpyPqaPTvVYbaHVZNFyoXDXS8hlpoBAoZSoApg64Hp6EvIv+YMHoPLF65EcP2zJziJ2z8CnELLBgzS+I/l4gzTYY4mfzcx1M4zJ6gMhUuc3mXKf7eZcTJENjKXqLJ8OlIOnrFW1kRxzGjBmV9nid3mWAuI0cIerogc1lQMKZq5y5jvD9nLusMpYfvuOz7+PENLwEQzWVFIcMgK3PMY9q0aTltTBHZYdSwfljwx6mhjmVR5hlytBBpS5pMR64IowXiZGQuzEBmc5kz+VmTiDiZAjbxb3My4nkyTSaMp2B78Y+rj5PWs88VLK2OEzKCuYyyGtD78jeXqa5gS3mCTNPFHTEX5g5cHBF6divBvoN7YO2GOrcm0wm0rEIisEffdttthWpHEXkGraL0DKoMcQtpPXgCKAQc7zI9r95BorYWDWku82gyMiGjG4iImgw7LrhoWb5Q3bcir9f3BmO63yMJAtLaThu/r/Q6mqoglTZ8S3ZrqupyYeYTZHa0FkjgE9NmMg/urihyMt8RqGE1GcVJ9Q90rCZDrtktyXRe+QlxoievtqDy1wBchLSM+H/q1bXOap17j6ZpfYd8J/7sKFieds7ffn0uFtUCNfFIREVLIu2fu8zObeZc3amM2Rk4GcBps6Z8d4n/zvElisg7aHxmisQnbkFvY8R/LkEr3ebWPAsZ4RnLSqwcfU2tKdnhDKJXk8jJzLPLLLck0p73aJjWCryjPcjyAUUNDsYMi6imIpU2OFdxGfFvMJWST5DZGTgZwOlbpO0C3z1NpnN8iSLyjrCajCJoMh1pP2aJJVtTeY1+FwUYZcluziBkvMS/e/++duG5Myfs5xUyNpewG8oYWxv2j5MJi2hEdZvLxGqvqluTUYBO58LMJ6btbKa8QiHUl9i6dWtW24vofKCa390ylDKm0rmkyUQ6gyaTyK8mA1iC4I7LrKzi5Ebc1JJBk+GyMItkN2DF94zcpw96divxCBmdCZndb8KRJchsy6QfjahI6f7lly0XZ9Pl4szSynQSTYYl7OTjZHbDbx6EUJzMCSecII3uP/nkk7Fs2bKcNebhhx/G3LlzEY1GoaoqnnnmGQDAjTfeiKVLlyIWi6GsrAzXXnstRo4c6Tl/3rx5uPXWWzFw4EAAwKBBg/C3v/0tZ+3ryjjvxANw0L59MXxI78DjqGhZujO4MNueVpZZKb/3Ov/EA9hv0mSa7EqWALB5WxNeW74BZx+/vxOfJGZhFiiclkQavSutGBMx4NOwCevdcb6xPBSdv63CbeEyW/OIRjSk0zqu+8cSAPI8bwbnVOB2Yc6f91w2YMS/nXqI3/ZdQSghI7PjNzY25nQVtnDhQrz44ot48sknUVFRgW3btrF9P/jBD3DNNdcgGo3itddew4wZM7Bo0SLpdY466ijcc889OWvX7oKIpmLU/t56LCLI1MHMZR2YAkNTFcRjGhJJvaAr/jLSoDhN5rf3voXt9a04eewQVFbEAcDFFcjiZFoTaZRSMkjNca1N6+ZurcmI70LPkJ7HD2QuI8g0GZd3GdDpNBneu4y+9W74yQMRKGSOOeYYKIqCRCKBcePGufbV1dXh5JNPzllDHnjgAVx++eWoqLDcK/v06cP2jR8/nv0+5JBDUFNTA8Mw7CjqInIJ5l2mG8wM1JEojUXy7sIsQtNUlMY1NHKczPb6VgBufsEQCGeZuYw85ChnXEksgsaWFL6u2WVnYfben7JAd1V44mQMk+WDywbRiIokJ2REIc6EDAv573xpZXgehr717riwCEKgkLnjjjtgmiYuvvhizJo1i21XFAW9e/fG3nvvnbOGrFu3DqtWrcLdd9+NZDKJs846C2eeeabnuLlz52LcuHG+AmbZsmWYOnUqKioqcNFFF3mEYxHBoLooab1zCPHSeAR1jYmCD8yykiiaW9Ke7WkusJAn/kW3XcDKVEC8EsWKlJVG0diSwjX3vm2d68nDDPzftROwc1f7qn12JEROxjDNNhXSikZUFoh78L59MHyIO7M3ZQQA0yidST3WWTQZzoU5bLmN3Q2BQmbMmDEAgHfeeQelpaXtutGpp56KTZs2SfctWbIEuq5j8+bNePTRR7Fz506cffbZGDJkCEaPHs2Oe/7557FgwQLf8gLjxo3DSSedhJKSEnzyySe46KKL8NBDD2GfffZpV9u/SyDvsrRudoqo6ZI4leot7H3LSqJSF2Zew+Aj/hXFbVY2TROtiTQrkU0r8oqSKLZw15NpaL0rS9G7sn3jrSMhcjKGbrbJbTcqJGeV5i7j0s5AUfCjifth49ZGHHPYIDz39vo2tT+X4EtsFM1lAdA0DXfddReee+451NXVYfny5Xjrrbfw1Vdf4bzzzgt1o/nz5wfur66uxuTJk6GqKnr37o2jjjoKq1evZkLm5Zdfxl133YU5c+a4TGk8evVyVjrDhw/HqFGjsHr16qKQyQKqArz/aS3e/7S2o5sCwMlKXGhNpqI0yrzLWhOORsMLGUb8q4rHbTeVtlLUkxt2KkWajHvIdaaywLmCKHB1w2yTVsxrP3ziUAIJLkpbowAY0Lscs375fWyxE1MCwP3XTcz63rkCHyfDBM53TMqE+vK33HIL1qxZgzvvvJMN9n333RePPfZYzhoyefJkLF68GADQ3NyM5cuXY9iwYQCA1157Dbfddhvuv/9+DBrkn7CvttaZGDdu3IiVK1di//33z1kbvwvobPbi0pJwVRRzjbKSCIuT4RNl8oGFbuJfAZ89pcUWTCQkk2nL7FNuB3oSOtfbzg1kaWXapMlwHmJ84lB2H/uaacNbOZXPzdYvRA2kfEFxcTJFTcYXr7zyChYuXIiysjK2Iunfv79rUm8vLrjgAvzud79jzgRTp07F2LFjAQC//e1vEY1Gcdlll7Hj58yZg549e+Laa6/Fsccei+OOOw5z587FK6+8Ak2zOtjMmTMxfPjwnLXxu4DOtsoqZZpMge8bj6BmexMAt/aSlhDRiuLEFxGoBk6pbe6jFDXkHk3obEI9FxD5KUuTsZ5z/xAZwwm8h5hMyJDnI9NkuHcZplpsIaAxHgZF4j8I0WjUk9p/x44d6NGjR85j+E1oAAAgAElEQVQaUlJSgjvuuEO675133vE975ZbbmG/Z86ciZkzZ+asTd9FdLQ3mQiHkylsu0rjEaaN8KvyNKeuUFwMZf81XULG1mTsyTFtjx+vkMl92zsaYrJQw7A4mUdunMTeRxhkFDI2Z0iLAP5V5jPLdDZwJcj8jhL/ocxlkyZNwlVXXYUNGzYAALZs2YKbbroppy7MRXQOdLb+z0r1FlqTKYmgJWEJBt6jTKbJOOWXre1rN+xEQ1MSgGMuSxAnI3ALu+OqVubCrKkKKivirEZQGGTWZAQho3j3dTRkEf+74ScPRCghM2PGDAwaNAinnHIKdu3ahRNOOAH9+vXDL37xi3y3r4gCo7OtspiJocCTRmksgtZk2gpM5TkZ3e1BZrVRYWR3U0sKM//8Jm5+0MqEEbNLDdPKXuRkOslcmFPwyUKXfrgZNdub2pQDL/r/27vz8Jru/A/g73tvVr0qi4SEFE1rGXkQBBOSpyKVGGkWfqIU0bFNtaqmLbEby2C0gx8pj/0ZP1pLI1EyREoJyoSktunMGA8eJGS1Zr33nt8fN+fcc9fcLGfJzef1D7nn5pzvOffmfM73+/ku9Uz8yzHDxQYWFW+CTLm1FgjNrrqri4sLFixYgAULFqC0tBSenp4O+QRG5PeUxfXOEfm47q5OYBh9boWfk3lSVo47D58isKOHUeKffXqvrl0qmu2ZZjpjQiuTICPHG2NjsUtRMwyDdf93BTUaHXw86p9853dhtpz412/f+/dfa39uYIFFwA8sLe3eaVeQYZvJWK9e6ROiLi4u8PHxkcWgPdI05PYHwO8CKia2V1tFlcaoR9mmg78AAH74Os5sxL+OMW5aA8xXaFSb5GQc8U+H/ax0DLhpYRpynvzeZW4WVgxlazLX/8tOQWX+HenR2cvsNSkolQowvAlVWxK7gsy7775rltg0dM1TIiIiAkuXLrU6foU0H3JrLpMqWco+OVdUacyWD2ZZai4zXQXStCbjbtbsI6/r3RTYU+Y3MzbkIYHfXGapicl08lbTQ3y/JkZGuRlDzk5uf2NCs+v5YsWKFYiJiUFmZiauX7+OkydPIi4uDkuXLsXRo0eh0WiwfPlyoctKRCC377+Kq8mIe1x+kNHoLM8jxr9pKGvHyZjOOWa2tLNJbkIm98Amxd5EjSa3bNA4Gdu3J9MAYnoEF2eVpOsh8fEH6zriAFxb7KrJbNq0CadOnYKrq3722U6dOmHp0qWIiorCuXPnsGbNGgwfPlzQghJxyC0pKVlzGS/IWHvyNNw0+CuKmjaX6W9yvwvtjIyL98yvr7wud5Ngrxc/4Dbk6b2u+c7MAojcnpB4+FPtyLiYgrArzOt0Ojx8+NDotfz8fG4tB3d3d7NxNKR54t8M/jTttxKWRI+/sqCYjJrLrNRkLCX+a0xrMrVB5aPRvfHD13FmT9+O2HSisBBkGnKabE2mjdryQnvm17L+xxCLUml4KHHEz9wWu2oySUlJSEpKwujRo9G+fXs8fvwYqampmDRpEgDg3Llz6NOnj6AFJeJgv/9t1C7o273u9WeEJlXNigsylRqr08Ybjfhn1+Exay4zaR4zbeJxwBsO+0Bgay0Ye7BB/PXXXC1uN28uk++1VCkU0DDseB75llMIdgWZadOmoVu3bjhx4gRu3boFHx8frFq1CuHh4QCAyMhIREZGClpQIg6uX79MHgvZm7KFdfMExQaZymqNxTEaDMNwvYXYEf/29C4z5Yj3m6bKyXi21geXUe+8ZXG72YJ6MryWXO1FyU/8S1ggCdQZZLRaLaKiopCRkcEFFeK4uPUvZJQwBcQPMtxAPx1j1IWZpdUxJol/gNHV3bvMtGOAIz7VNlVzWRu1K374Os7qdrOajIwvJX8WBEf8zG2p806iUqmgUqlQVdV8F1Ei9mO//04yGcBheAIWN8qwx9XpzJP5gP4Gas84GdPeZab7csTbDXvO7MBUQKA8hGkfChnfvPmzIMi4mIKwq7ls0qRJ+OyzzzBjxgy0b9/e6MMMCAgQrHBEfIaajDz+EqSqyRgGFDIWl0LW6RijRC47TsasC7PJ03ZLqMmwOSx25mlAmCDDb44D5B2w2cUAAUr8W7RixQoAwIULF4xeVygU+PXXX5u+VEQy7BO8bNZIZ3MyEh1Xp4PF3mUaLcPNwszOsKuzkPg3vY5vtG9t9LMj3m/Yc67i1WSECKb8/euP0eSHaDJKJYxyeC2JXUHmX//6l9DlIDIht0n8uFY7kaMMe/qMhbEvgH40u/F6MoZlq/lMc1vebdzxw9dxmPXVGdwreO6QSWB2wGlVNa+5TIBnluoa02ET8r6YLTXxL4/HVSIb7FNWXb2ixKLiNVuJiW3S0OkYaKwk/o2by8x7VOm3Wd6/Iy9gxTa1VtUYlq0W4jwH9myP3m8bprKS+82bRvzboNFosH//fuTk5KCsrMxoDrN9+/YJVjgiPi4nI7PEv2TNZRaawAA28a//P3/99hqNaROO5RuKI68two7UN6rJCHCirdycsfIPg/He5+kA5Bmw+d/blpr4t+tOsnr1ahw4cAD9+/fHrVu3MHz4cJSUlGDQoEFCl4+IjOtdJrOcjNiZf37in+3CzJ9Li5/4ZwdjAsbJbtv7Nz6OI7GUkxGl+VXWl7LlJv7tupNkZmZi+/btSEpKgkqlQlJSElJSUnD58mWhy0dExt4MZNe7TOzj8gaBsjUZ/o1So9UZNZcZBiDaN70SV5NpshLLh6WcjBj3VblfSxonY0NlZSX8/PwAAG5ubqioqEBgYCD++c9/Clo4Ij4a8V973NrT1+kYLpnPfwLlD8ZU1M5dBgDVGvtqMkqqyTQ5WV5L3vc25DftAQB9uvpIVBhp2MzJHDt2DDExMQgMDMSNGzfQq1cvBAUFYdOmTVCr1WjXrl2TFWTv3r3Yt28fnJ2doVQqkZ6ub2dNTk7GxYsX4enpCQCIjo7GRx99ZHEfKSkpOHLkCAAgISGBloduACeZdmGWornMMLOyPnDwA69Wy0v8K2E18W91/3DknExt4l/gnIwpuV/Lnm9625zBwFHZDDJLlixBTEwMFixYAJVKv0pdcnIyli1bhlevXnHjZxorMzMTJ06cwOHDh6FWq1FcXGy0ffr06ZgwYYLNfeTk5ODEiRM4duwYAGDMmDEYMGAAQkJCmqSMLcVrtSs3yqYLM2+VRbEpFArodAyg0N/A2qhd8LJ2WWWNznLi37xbrbV9G37X0VgeJyP8cWU5QaYMiyQ2m0GGfVLr1asX91rnzp2xZ8+eJi3Erl27MHv2bKjVagBo0AqbGRkZiI+Ph5ubGwAgPj4eGRkZFGTqSd1KP6266UA3qUg1rQzAzqysDygqpRJtPdzxqEi/9Di/JqNQGLpa212TkWjFTzE4WRwn00KTMhI8HMmNzSCj0+lw6dIloy7Lpn7728avOXLnzh1cu3YNGzduRHV1Nd5//30kJiZy23fv3o0DBw4gICAAn3/+OQIDA832UVBQgAEDBnA/+/n5IScnp9Fla2nYNegrKjV1vFMcUuVkAH3e5OcbBfBu4wYnlQLebdy5bVqdjrdmu4Ib+1Dfmowsb4yNxPbCqxJ67jITcr6UDvgsYTebQaa6uhoLFy60GmQUCgV+/PHHOg+SkJCA/Px8i9suXrwIrVaLgoIC7N+/H2VlZRg3bhy6dOmCkJAQzJkzBz4+PlAqlUhLS8PUqVORlZXFNd+RptW6VW2QqZJJkJGodxmgD3CPil7iUdFLvObujLYehiCzeOtF4+ayBtdkmrbMcmCpJiNGs6Aj1godgc0g4+7ublcQqQubjLfG398fMTExUCqV8Pb2RmhoKK5fv46QkBCjzgXx8fFYvXo1Hj9+jA4dOhjtw8/PzyiQFRQUcD3iiP3Y5jK5BBku2S5RToalVAAxg7vg+9O3jXqWsdv4iX9nJ2WdwUbpwFUZi73LxDhNGV5KKWrgciOLLkQxMTHIzs4GAJSXl+Pq1avo3r07AODJkyfc+7Kzs6FUKi32aouOjkZaWhoqKytRWVmJtLQ0jBgxQpwTcCDq2ppMZbU8goxhxL8EORnenfFFeQ08X3fD17PN11RSKBRgO+NVa7Rwda67ls3NESfDG2NjGUb8G75D4nRhFvwQpAHsSvwLbfLkyVi8eDFGjhwJAIiLi8PgwYMBAPPmzUNJSQkUCgXUajW2bNkCJyd9sRcuXIiIiAgMGzYMAwcOxPDhw7l9xMfHG+VoiH1aszUZueRkuDnEpDi2+WuWFnNjJ8gEgJoandHMAHVxxHmsnLi5y8RtLpNl77Ja8i2Z8GwGmby8PFEK4ebmhnXr1lncZqsn26pVq4x+njVrFmbNmtWURWtx2MS/vYMKhWaYQk3amgzL0iBV/gSZ1RqtXauKssHTEW8+FmdhbuHjZFpyq5ksmsuIfLjUNvWMj+oucUn02Ju3FG3blp6+LQ1SVSgNif9qjc6uGawdeZyMUqkfyCpWToZ9GJDjtfT10ncWYVsIWiK7ZmEmLYucRiVLOSiUDRwxg7tg4u96ALBWkzG8V6PR2TVbgiM2k7H0OSqlaONklAoFdDKtK4wb3h2BHT3Qr7uv1EWRDNVkiKxJ3YUZANxcndDKTd+MaGniUP7cZVXVWvuCTO2/YuU9xebspBAtJ8N+JjKsyMDZSYnBvfxlWcsSCwUZImuGLsxSjPg3KQMsr7PDn1bmeXk1NzWPLVI2A4rBSaU0Ojch77HsgwiNk5EnCjJE1gyLh4l/bG7AJC/IWMq38MfJvKqo4TpP2GKYk80xo4xpbU7IWb25fVOMkSXKyRBZMzydSncz5gcZy12YFUbvUbdyxrjh3eDf9jWr+1RIV0EThZNJN24hm4u4xL9gRyCNQUGGyJqUc5exhzRuLrN8K+M31bRu5VJn7zzD2x0zypjWZATNyci4dxmh5jIic4YR/xLgrXzJsjYGhv8ee5rLDMs7N6aA8mUaZCykspqMXBbYI5ZRkCGyJmHenwts/KYwpQJo59UKSSN/Y/Re/k3UviBTewwHbS9zNg0yIjSXUeJfnijIEFmTamVM/iH5T8oKhQI7Fr6L/4l42+i9/KYatR0D77jeZfKYWKHJKU06SIiRk6GkjDxRkCGyJmXvMq65zI7mGNPEf53v58b/OGZNxrQJS8jBmCpK/MsaBRkia3LrXWb1PbwndbvGydT+66g5GdOmK2GnldHfxijxL08UZIisyaF3mbW2/jc7tOH+z3+PaT7CIsOQ/waWTt5MZ0YQp3eZYIcgjUBdmImsqSTsXWYpJ8O35uMheFFeDcA48V+fWZgdtSZj1lwmZE6mdt9aR72YzRwFGSJrSklHLdrOybi7OsHdVf8nxH9St6dLraP3LjNrLhOwzYTtZKCjICNL1FxGZE3ScTImZbD3PXZNkOngc5eZ1uaErMmwQZ2CjDxRTYbImqQ5mTqay/iMZgWwYz2Zse92xf3HzzEwqH2DyydnptdM0C7M1FwmaxRkiKxJOcDO0mBMa+rbXObfVo0Nc95pYMnkz/SaiTEYk2oy8kTNZUTWpFy0jCuDHTdIfjHtaS5zdGZBRoRxMhRk5Ek2NZm9e/di3759cHZ2hlKpRHp6OgBg8uTJKCsrAwBotVrcvn0b6enp6N7deALCy5cvY/r06ejcuTMAwMXFBYcOHRL1HEjTkzTI1KO5zKgmQ0HGQnOZ8Mei5jJ5kkWQyczMxIkTJ3D48GGo1WoUFxdz2/bs2cP9PysrCxs2bDALMKzAwECkpqYKXVwiImmby+wf8c+/qTrJoPYlNTFzMu8P74bbD56i6xsegh2DNJwsgsyuXbswe/ZsqNVqAEDbtm0tvu/w4cMYPXq0mEUjEpOyJsMm/uvbu4xqMuYriAo5U/Jvunjj25W/E2z/pHFk8ddw584dXLt2De+//z5GjRqFgwcPmr2nqKgIP//8M+Li4qzu5969e0hISMCYMWNw5MgRIYtMRCJpa1lDm8uoJmMWmGk0fsslSk0mISEB+fn5FrddvHgRWq0WBQUF2L9/P8rKyjBu3Dh06dIFISEh3PvS0tIQFhYGLy8vi/vp2bMnzp49i9atW+PBgwf48MMP0a5dO4SGhgpyTkQc7M377QApmkLqMUEm7y4qh84KUhOzuYzImyhBpq5ahb+/P2JiYqBUKuHt7Y3Q0FBcv37dKMikpqZi7ty5VvfBNrUBQEBAACIjI5Gbm0tBxgH87+fvwNezlWTHt6t3mSzaBORDzFmYibzJ4k8jJiYG2dnZAIDy8nJcvXrVKLmfm5uLFy9eIDw83Oo+CgsLuSk6nj59igsXLljtIECaly7+beya2bipGZrL7J+LjOiZNZdJVA4iPVkk/idPnozFixdj5MiRAIC4uDgMHjyY256amor4+HioVCqj39u4cSN8fX0xbtw4ZGZm4ttvv4WTkxO0Wi3i4+MRGRkp6nkQx2IYjFn3e+lJ3RhdD8KSRZBxc3PDunXrrG5fuXKlxddnz57N/X/ChAmYMGFCk5eNtGD1WLSMcg7GqPMDYcmiuYwQOaprPRk+enI3Rt24CYu+CYRYweVk7FofRuDCNDOUoyIsCjKE1MGeAEI3VWP2zERNWgYKMoRYVY9xMlSVMUI5GcKiIEOIFfXpwkyJf2MUZAiLggwhVtRnPRmqyRij60FYFGQIqUN915MhFGSIAQUZQqww9C6jcTL1ZU8TI2kZ6JtAiDXsYEwKIPVmWpOh5cRaLgoyhNSBmn7qjxL/hEVBhhAr2KdvumHWn+kloyvYclGQIcSK+qyMSWzzbuMmdRGIRGQxQSYh8mT/YExijA3QEf0DMGbY2+jo21raAhHJUE2GECu4mgwl/htMqVBQgGnhKMgQYsX4KP2id5STIaThqLmMECsSI7siMbKr1MVolqjLMmFRkCGkiXi2dsWQPh2kLoYsMBRlSC0KMoQ0kb8ti5a6CLJD6SxCORlCCCGCoSBDCBEAtZcRPVk0l02ePBllZWUAAK1Wi9u3byM9PR3du3dHRUUF5s+fj1u3bkGlUmHevHkYOnSoxf0cPHgQ27dvB8MwCA8Px6JFi6CkifoIIUQysggye/bs4f6flZWFDRs2oHt3fffRnTt3Qq1W49SpU7h37x4++OADZGZm4rXXXjPax4MHD7B582akpaXBw8MD06ZNw9GjRxEfHy/mqRBCeGh2aiK7x/zDhw9j9OjR3M9///vfMXbsWABA586dERQUhHPnzpn93smTJxEZGQkvLy8olUqMGTMGGRkZopWbEGIQ2MEDABDczUfikhCpySrIFBUV4eeff0ZcXBz3Wn5+Pjp0MHQL9fPzw+PHj81+t6CgAP7+/tzP/v7+KCgoELbAhBCL3grwwIFVv8OQ3tSlu6UTpbksISEB+fn5FrddvHgRKpUKAJCWloawsDB4eXmJUSxCiIBauTlLXQQiA6IEmSNHjtj1vtTUVMydO9foNX9/fzx69IgLPAUFBRg4cKDZ7/r5+RkFsvz8fPj5+TWi1IQQQhpLNs1lubm5ePHiBcLDw41ej46OxoEDBwAA9+7dw40bNxAWFmb2+1FRUcjKykJpaSl0Oh0OHTqEESNGiFJ2Qgghlsmidxmgr8XEx8dzTWesKVOmIDk5Ge+++y6USiWWL18OtVoNANi4cSN8fX0xbtw4BAQEYObMmUhMTAQADB48GLGxsaKfByGEEAMFw9AsQwDw8OFDDBs2DD/++CM6duwodXEIIaRZqOveKZvmMkIIIY6HggwhhBDByCYnIzWtVgsAFsfgEEIIsYy9Z7L3UFMUZGoVFRUBAD744AOJS0IIIc1PUVEROnXqZPY6Jf5rVVZW4ubNm/Dx8THr4UYIIcQyrVaLoqIiBAUFwc3NzWw7BRlCCCGCocQ/IYQQwVCQIYQQIhgKMoQQQgRDQYYQQohgKMgQQggRDAUZQgghgqEgQwghRDAUZJrA3bt3MXbsWERFRWHs2LG4d++e1EVqtLVr1yIiIgLdunXDf/7zH+51W+fa3K9DWVkZpk2bhqioKLz33nv45JNPUFpaCgD45ZdfEBsbi6ioKPz+979HSUkJ93u2tjUHM2fORGxsLOLj4zF+/Hj8+uuvABz7s2Zt3rzZ6DvuyJ9zREQEoqOjERcXh7i4OGRnZwMQ4ZwZ0mgTJ05k0tLSGIZhmLS0NGbixIkSl6jxcnJymPz8fGbo0KHMv//9b+51W+fa3K9DWVkZc+nSJe7nNWvWMPPnz2e0Wi0TGRnJ5OTkMAzDMCkpKUxycjLDMIzNbc3F8+fPuf+fOnWKiY+PZxjGsT9rhmGYmzdvMlOmTOG+447+OZv+LTOM7fNqqnOmINNIxcXFTL9+/RiNRsMwDMNoNBqmX79+TElJicQlaxr8L6atc3XE63DixAkmKSmJuXbtGjNy5Eju9ZKSEqZPnz4MwzA2tzVHR44cYRISEhz+s66qqmISExOZBw8ecN9xR/+cLQUZMc6ZJshspIKCArRr146b70ylUsHX1xcFBQXw8vKSuHRNy9a5MgzjUNdBp9Ph22+/RUREBAoKCuDv789t8/Lygk6nw9OnT21u8/DwkKLoDbJw4UJcuHABDMNgx44dDv9Zb9y4EbGxsUaLbLWEz/mLL74AwzDo168f/vjHP4pyzpSTIcSCFStWoFWrVpgwYYLURRHFqlWr8NNPP2HOnDn4y1/+InVxBJWXl4ebN29i/PjxUhdFVPv27cPRo0fx/fffg2EYLF++XJTjUpBpJD8/Pzx58oRbS0Gr1aKwsBB+fn4Sl6zp2TpXR7oOa9euxf3797FhwwYolUr4+fkhPz+f215aWgqlUgkPDw+b25qj+Ph4XL58Ge3bt3fYzzonJwd37tzBsGHDEBERgcePH2PKlCm4f/++Q3/O7Ofj4uKC8ePHIzc3V5TvNgWZRvL29kaPHj1w7NgxAMCxY8fQo0ePZtNsUB+2ztVRrsNf//pX3Lx5EykpKXBxcQEABAUFobKyEleuXAEAfPfdd4iOjq5zW3Pw6tUrFBQUcD+fPn0abdq0cejPevr06Th//jxOnz6N06dPo3379ti5cyemTp3qsJ9zeXk5Xrx4AQBgGAYZGRno0aOHKN9tmuq/Cdy5cwfJycl4/vw5Xn/9daxduxZvvvmm1MVqlJUrVyIzMxPFxcXw9PSEh4cHjh8/bvNcm/t1uH37NmJiYtC5c2duXYyOHTsiJSUFubm5WLp0KaqqqtChQwesW7cObdu2BQCb2+SuuLgYM2fOREVFBZRKJdq0aYN58+ahZ8+eDv1Z80VERGDr1q3o2rWrw37ODx48wKxZs6DVaqHT6RAYGIhFixbB19dX8HOmIEMIIUQw1FxGCCFEMBRkCCGECIaCDCGEEMFQkCGEECIYCjKEEEIEQ0GGEAEEBwfjwYMHUheDs3//foSGhiI4OBhlZWVSF4e0IBRkiMOJiIjAxYsXAQCpqakYN26coMebOHEiDh06ZPRaXl4eAgICBD2uvWpqarBmzRrs2rULeXl58PT0NNr+8OFDdOvWDdOmTTN6/YsvvsCmTZsAWL+O7LWeOnUqgoODERwcjJ49eyIoKIj7ecmSJQCArVu3IiIiAsHBwQgPD8dnn30m0BkTOaEJMgmxQaPRwMmpef+ZlJSUoKqqCm+99ZbN912/fh25ubno27dvvY+xY8cO7v/Jyclo164d5syZw7125MgRpKenY8+ePXjjjTdQVFSE06dP1/s4pPmhmgxxWHfu3MHSpUvxyy+/IDg4GP379wcAVFdXY+3atXjnnXcQGhqKJUuWoLKyEgBw+fJlhIeHY9u2bRg8eDDmz5+PZ8+eYcaMGRg0aBBCQkIwY8YMPH78GACwfv16XLlyBcuXL0dwcDA36WC3bt1w//59AMCLFy8wd+5cDBo0CEOHDsU333wDnU4HwFBDWLt2LUJCQhAREYGzZ89y55Camophw4YhODgYEREROHr0qMVzra6uxqpVqzBkyBAMGTIEq1atQnV1Ne7evctNBRISEoJJkyZZvV5TpkzB+vXrG3PJrbpx4waGDBmCN954AwDg4+ODsWPHCnIsIi8UZIjDCgwMxJ/+9Cf06dMHeXl53BxMX331Fe7evYu0tDRkZmaisLAQKSkp3O8VFxfj2bNnOHPmDFasWAGdTodRo0bhzJkzOHPmDFxdXblgMmfOHPTv3x9LlixBXl4e1zTEt2LFCrx48QJZWVnYu3cv0tPT8f3333Pbr1+/ji5duuDSpUuYOnUqFi5cCIZhUF5ejpUrV2L79u3Iy8vDd999hx49elg81y1btuDatWtIT0/H0aNHcePGDXzzzTfo0qULN8dYTk4O/va3v1m9XuPHj8e9e/e4psam1Lt3b6Snp2PHjh24ceMGN7kmcXwUZEiLwjAMDh48iAULFsDDwwNqtRozZszA8ePHufcolUp8+umncHFxgZubGzw9PREVFQV3d3eo1Wp89NFHyMnJset4Wq0WGRkZ+Pzzz6FWq9GxY0d8+OGHRjUSf39/JCYmQqVSISEhAUVFRSguLubKcvv2bVRWVsLX1xdvv/22xeP88MMP+Pjjj+Ht7Q0vLy98/PHHVms91ri5ueEPf/gDNmzYUK/fs0dcXBwWLVqE8+fPY+LEiQgNDcW2bdua/DhEfpp3YzMh9VRaWoqKigqMGjWKe41hGK75CgA8PT3h6urK/VxRUYHVq1cjOzsbz549A6CfvVir1XILd1lTVlaGmpoao8Wf/P398eTJE+5n/oSD7u7uAPSz5vr4+GD9+vXYtWsXFi5ciL59+2LevHkIDAw0O05hYaHZMQoLC+u8HqbGjBmDnTt3muVLVCoVNBqN2ftramrszlnFxsYiNjYWNTU1yMrKwpdffokePXogLCys3uUkzQfVZIhDUygURj97enrCzc0Nx48fx5UrV3DlyhVcvXoVeXl5Vn9n165duHv3Lg4ePIjc3Fzs27cPgD441cXT0xPOzs5G63Kwq07aIywsDLt371wvrXYAAAJBSURBVMb58+fx5ptvYvHixRbf5+vra3YMX19fu47B5+Ligk8++QQbN240Oj9/f39uVUxWRUUFSktLjYKbPZydnTFixAh07doVt2/frncZSfNCQYY4NG9vbzx58gTV1dUA9M1PY8aMwZ///GeUlJQAAJ48eYLs7Gyr+3j16hVcXV3x+uuv4+nTp9i8ebPR9rZt21odE6NSqRAdHY3169fj5cuXePToEXbv3o3Y2Ng6y15cXIysrCyUl5fDxcUFrVq1glJp+U925MiR2LJlC0pLS1FaWoqUlBS89957dR7Dkri4OFRVVeH8+fPca71794aLiwu2bduGqqoqlJeX4+uvv0ZQUBA6dOhQ5z5TU1Px008/4eXLl9DpdDh79iz++9//olevXg0qI2k+KMgQhzZo0CC89dZbGDJkCAYOHAgA+PLLL9GpUyckJiaib9++mDx5Mu7evWt1H0lJSaiqqsKgQYMwduxYs+adSZMm4eTJkwgJCcHKlSvNfn/x4sVwd3dHZGQkxo8fj5iYGIwePbrOsut0OuzZswdhYWEYMGAAcnJysGzZMovvnTlzJoKCgrgmqZ49e2LmzJl1HsMSlUqFTz/9FE+fPuVeYwPMP/7xD4SHhyMyMhKFhYXYsGGDWc3PErVaja1bt2Lo0KHo378/vvrqKyxbtozr8UccF60nQwghRDBUkyGEECIYCjKEEEIEQ0GGEEKIYCjIEEIIEQwFGUIIIYKhIEMIIUQwFGQIIYQIhoIMIYQQwVCQIYQQIpj/B3M4ZqvpldQvAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "init_key, sample_key = random.split(random.PRNGKey(0))\n",
        "init_params = tuple(dist.sample(seed=init_key)[:-1])\n",
        "\n",
        "@jit\n",
        "def run_chain(key, state):\n",
        "  kernel = tfp.mcmc.NoUTurnSampler(target_log_prob, 1e-3)\n",
        "  return tfp.mcmc.sample_chain(500,\n",
        "      current_state=state,\n",
        "      kernel=kernel,\n",
        "      trace_fn=lambda _, results: results.target_log_prob,\n",
        "      num_burnin_steps=500,\n",
        "      seed=key)\n",
        "\n",
        "states, log_probs = run_chain(sample_key, init_params)\n",
        "plt.figure()\n",
        "plt.plot(log_probs)\n",
        "plt.ylabel('Target Log Prob')\n",
        "plt.xlabel('Iterations of NUTS')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TL-KmNG8molC"
      },
      "source": [
        "Let's use our samples to perform Bayesian model averaging (BMA) by averaging the predicted probabilies of each set of weights.\n",
        "\n",
        "First let's write a function that for a given set of parameters will produce the probabilities over each class. We can use `dist.sample_distributions` to obtain the final distribution in the model."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sRkYo3z1lox5"
      },
      "outputs": [],
      "source": [
        "def classifier_probs(params):\n",
        "  dists, _ = dist.sample_distributions(seed=random.PRNGKey(0),\n",
        "                                       value=params + (None,))\n",
        "  return dists[-1].distribution.probs_parameter()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EcaE23RSnHP3"
      },
      "source": [
        "We can `vmap(classifier_probs)` over the set of samples to get the predicted class probabilities for each of our samples. We then compute the average accuracy across each sample, and the accuracy from Bayesian model averaging."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dS01h9X3nBzh"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Average accuracy: 0.96952\n",
            "BMA accuracy: 0.97999996\n"
          ]
        }
      ],
      "source": [
        "all_probs = jit(vmap(classifier_probs))(states)\n",
        "print('Average accuracy:', jnp.mean(all_probs.argmax(axis=-1) == labels))\n",
        "print('BMA accuracy:', jnp.mean(all_probs.mean(axis=0).argmax(axis=-1) == labels))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C3wK_Yfcngz-"
      },
      "source": [
        "Looks like BMA reduces our error rate by almost a third!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TYamCA8E3jle"
      },
      "source": [
        "## Fundamentals"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UbFn9vIS3nIa"
      },
      "source": [
        "TFP on JAX has an identical API to TF where instead of accepting TF objects like `tf.Tensor`s it accepts the JAX analogue. For example, wherever a `tf.Tensor` was previously used as input, the API now expects a JAX `DeviceArray`. Instead of returning a `tf.Tensor`, TFP methods will return `DeviceArray`s. TFP on JAX also works with nested structures of JAX objects, like a list or dictionary of `DeviceArray`s.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rmdg7MvylrBP"
      },
      "source": [
        "## Distributions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uME3nS_iRybJ"
      },
      "source": [
        "Most of TFP's distributions are supported in JAX with very similar semantics to their TF counterparts. They are also registered as [JAX Pytrees](https://jax.readthedocs.io/en/latest/pytrees.html), so they can be inputs and outputs of JAX-transformed functions."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "15xO-noWem0d"
      },
      "source": [
        "### Basic distributions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J5ir3s5hlukJ"
      },
      "source": [
        "The `log_prob` method for distributions works the same."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6zCEN_fhlszJ"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "-0.9189385\n"
          ]
        }
      ],
      "source": [
        "dist = tfd.Normal(0., 1.)\n",
        "print(dist.log_prob(0.))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3uTla3s-l8SO"
      },
      "source": [
        "Sampling from a distribution requires explicitly passing in a `PRNGKey` (or list of integers) as the `seed` keyword argument. Failing to explicitly pass in a seed will throw an error."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aifUEqgFksk-"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "DeviceArray(-0.20584226, dtype=float32)"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "tfd.Normal(0., 1.).sample(seed=random.PRNGKey(0))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Nn_hJLghq4FG"
      },
      "source": [
        "The shape semantics for distributions remain the same in JAX, where distributions will each have an `event_shape` and a `batch_shape` and drawing many samples will add additional `sample_shape` dimensions."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uyCZDoESrVfi"
      },
      "source": [
        "For example, a `tfd.MultivariateNormalDiag` with vector parameters will have a vector event shape and empty batch shape."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kihalWoWq1Kb"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Event shape: (5,)\n",
            "Batch shape: ()\n"
          ]
        }
      ],
      "source": [
        "dist = tfd.MultivariateNormalDiag(\n",
        "    loc=jnp.zeros(5),\n",
        "    scale_diag=jnp.ones(5)\n",
        ")\n",
        "print('Event shape:', dist.event_shape)\n",
        "print('Batch shape:', dist.batch_shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IDMQOHG3rb7F"
      },
      "source": [
        "On the other hand, a `tfd.Normal` parameterized with vectors will have a scalar event shape and vector batch shape."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "eqNCoHY3rg2U"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Event shape: ()\n",
            "Batch shape: (5,)\n"
          ]
        }
      ],
      "source": [
        "dist = tfd.Normal(\n",
        "    loc=jnp.ones(5),\n",
        "    scale=jnp.ones(5),\n",
        ")\n",
        "print('Event shape:', dist.event_shape)\n",
        "print('Batch shape:', dist.batch_shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yM_dS0-g_E7V"
      },
      "source": [
        "The semantics of taking `log_prob` of samples works the same in JAX too."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jy3tVYMN_BIG"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "(10, 2, 5)\n",
            "(10, 2)\n"
          ]
        }
      ],
      "source": [
        "dist =  tfd.Normal(jnp.zeros(5), jnp.ones(5))\n",
        "s = dist.sample(sample_shape=(10, 2), seed=random.PRNGKey(0))\n",
        "print(dist.log_prob(s).shape)\n",
        "\n",
        "dist =  tfd.Independent(tfd.Normal(jnp.zeros(5), jnp.ones(5)), 1)\n",
        "s = dist.sample(sample_shape=(10, 2), seed=random.PRNGKey(0))\n",
        "print(dist.log_prob(s).shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nvDiFv3G6rre"
      },
      "source": [
        "Because JAX `DeviceArray`s are compatible with libraries like NumPy and Matplotlib, we can feed samples directly into a plotting function."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FZ6iPEU13hG0"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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OFsxNBACc4zw8gQVPAaL6WhfiokMRExkqdxRZxUVrkJUcjbO1LHhiwVMAsDlcqG3qRWaQj95vKDbqYWqwYtjukjsKyYwFT37vXF0XRI8U9PPvNyzK18Pjkbiahljw5P9OmToQrlEhKT5C7ig+IT8jDhFhapy+bJE7CsmMBU9+zeORcPqyBYU5CVAogu/p1dtRKhUoytPhzBULl0sGORY8+bWrLb3oH3Ji/pwEuaP4lGKjDr2DI6hv53LJYMaCJ792ymSBQgAKcljwNyvK0wMAznCaJqix4MmvnbpsgTErPqgO95iK2KhQzE2L5Tx8kGPBk9/q6bejvq0fi416uaP4pMVGPWqbe9E76JA7CsmEBU9+65RpdHS6eB4L/nYeKDBAkr7+c6Lgw4Inv3XKZIFeG440fZTcUXxSVnI0dHFhOF5jljsKyYQFT35pxCXi/NUuLJ6nD8rDPaZCEAQ8WGDA+bou2EfccschGbDgyS9dvNYNp0vE4nlJckfxaQ8WGOBye3COe9MEJRY8+aWTpg5oQpQozImXO4pPm5elRVS4mtM0QYoFT35HkiScMllwf54OalVwHu4xVUqlAovnJeGUyQK36JE7Ds0yFjz5nUbzALr77FweOUUPFiRhyO7CpfoeuaPQLGPBk9+5seyvmAU/Jffn6RAaosSR6na5o9AsY8GT3zll6sDctFjERWvkjuIXNCEqLDbqcazaDJHTNEGFBU9+pX9oBLXNvZyemaZlC1PQNzSCGk7TBBUWPPmVM1cskCRweeQ0LcofnaapusBpmmDCgie/ctJkgTY6FNkpMXJH8SuaEBWWzEvC0ep2TtMEERY8+Q23OPrATrExiYd73IVlC5IxMOzExevdckehWTKlgm9oaEB5eTlKSkpQXl6OxsbGcde8+eabePLJJ7FmzRo888wzOHz4sLezUpAzNfTA5nBzc7G7tMiohyZEicPnOU0TLFRTuWjjxo2oqKhAWVkZ9u7diw0bNmDHjh23XDN//nz84Ac/QFhYGK5cuYK1a9eiqqoKGg1XOpB3nDJZoFYpsGBuotxRfJJb9KDTapvwmqJ8HY5Wt+NvnynkQ2JBYNKC7+npgclkwltvvQUAKC0txZYtW2C1WqHVaseue+SRR8bezsvLgyRJ6OvrQ1ISb4aRd5wydaBwTgLCQqc0Lgk6Iy4R1dcmnn4ZnYc345TJgqXzk2cpGcll0ikas9kMvV4PpXL0b3ulUgmdTgez+c57W+zZswfp6eksd/Katq4htHUNYwmXR96TeVlaxEaF4vMzLXJHoVng9ZusJ0+exOuvv47XXnvN2y9NQezEV5tlcXnkvVEqFHisKBWnL1swMOyUOw7NsEkL3mAwwGKxQBRFAIAoiujs7ITBYBh37blz5/CTn/wEb775JrKzs72floLW8ZoO5KTGQKcNlzuK31uxKA1uUULVhTa5o9AMm7Tg4+PjYTQaUVlZCQCorKyE0Wi8Zf4dAKqrq/Hyyy/jV7/6Fe67776ZSUtBqXfAgStNVjxYMH5QQdOXlRyNjKQofHaa0zSBbkpTNJs2bcLOnTtRUlKCnTt3YvPmzQCAdevW4eLFiwCAzZs3w+FwYMOGDSgrK0NZWRlqa2tnLjkFjZOmDkgSWPBeIggCVixKQ21TL9q7huSOQzNoSssRcnJysHv37nHv3759+9jb7733nvdSEd2k6kI7EmPDEBaivOMywBGXOMup/NujRan4vx+a8PmZVjy/Ol/uODRDuN6MfJrN4ULN9W7cl52Ac3Vdd7wuLyNuFlP5v4TYMCyYk4hDZ1tQUZLHc20DFLcqIJ92trYTblFCdnK03FECwo2HoTqtNizK16Gjx4aj1eax93VabRi0cXVNoOAInnzasYtmRIarkZQQIXeUgHDzw1AKpQCVUoF9VfV4rCh17JqiPB2iwkPkikhexBE8+SyX24PTly1YODcRCk4heF2ISonslGhca+njDpMBigVPPuvi9W7YHG4U5enkjhKw8tK1GHGJaDQPyB2FZgALnnzW8RozNCFKGDO1k19MdyVVH4kIjQpXmnrljkIzgAVPPsnjkXCipgNF+TqEqLnr4UxRCALyMrRoMg9g2O6SOw55GQuefNK11j5YBxx8uGkWGLO0kABcabLKHYW8jAVPPul4jRkKhcDDtWdBbGQokhMicLnRCkmS5I5DXsSCJ590vMaMwpx4RHK53qyYl6VF/5AT7d3DckchL2LBk89p6hhAi2WI0zOzKDslFiEqBS43cJomkLDgyedUnW+HIAAP88ShWaNWKTA3PQ7XWvtgc/Bma6BgwZNPkaTRfcoLshMQF83zfGfTvEwtRI+EE5c65I5CXsKCJ5/SaB5Aa+cQHlnI0ftsS4wLQ3yMBofP8yCQQMGCJ59SdaEdCgE8EFoGgiDAmKlFU8cgGtr75Y5DXsCCJ58hSRIOn2/D/DmJiIkMlTtOUMpLj4NKKeDjE01yRyEvYMGTz6hv64e5exjLFqbIHSVoaUJVuD9Ph0NnWuHkISp+jwVPshq0Ocf2Id9/rBFKhYC5qTG37E/O05pm1/KFKRiyu3D0olnuKHSPuB88ycrucONsbSc8koTDF9qRpo9CXUvfLdfwtKbZlZ+pRVJ8OPYfa7xln3jyPxzBk09o7xrGsN2F3PRYuaMEPYUgoOTBTFyq70GLZVDuOHQPWPDkE+qae6FWKZBpiJE7CgFYtTgdKqWA/cca5Y5C94AFT7Jzix5cb+1DTkoM1Cp+SfqC2KhQLC1MxqenW+BwuuWOQ3eJ300ku0bzAJxuD3LTOdfuS1YvzcSw3YWq8+1yR6G7xIIn2dU29SJco0KKLlLuKHSTgux4pOoisf94o9xR6C6x4ElW/UMjaO4YQG56HA/W9jGCIGD1Q5mobepFfRufbPVHLHiS1fEaMzwSeO6qj3q8OA0hKgVvtvopFjzJZnTnyHboteHQcudInxQVHoJlC1Nw6GwLtxH2Qyx4ks3Vlj60dw9z9O7jvvVQJuwjIr48x10m/Q0LnmTzyclmhKgUmJPGh5t8WV5GHDIN0fjoWCPPbPUzLHiShcPpxpfnWlGUr0eoWil3HJqAIAj41tJM1Lf1o7a5V+44NA0seJLF0ep22BxuPLKA+777g8eKUhGuUaHycIPcUWgaWPAki4+ONiIlMYIbifmJcI0aqxano+pCG6wDDrnj0BSx4GnWNbT340pTL1Y/lAWBa9/9xpPLsuCRJC6Z9CMseJp1Hx1rRIhKgZWL0+SOQtOQnBCJRfl6fHSsES63R+44NAUseJpVNocLh860YNnCFESFh8gdh6ZpzbJs9A2O4MgFLpn0Bzzwg2bVF+faYB8R8a2lmXJHoTtwix50Wm23/VhyYgT02nC8f+gaFhn1/Evax7HgadZIkoQPquqRnRyDPO4c6bNGXCKqr3Xf8eO56XE4fL4Nl6734MFCwywmo+ma0hRNQ0MDysvLUVJSgvLycjQ2No67pqqqCs888wwKCgqwdetWb+ekAFB9tRtNHYNY80g2b676sfyMOKhVCnx6ulnuKDSJKRX8xo0bUVFRgQMHDqCiogIbNmwYd01aWhr+9V//FS+88ILXQ1Jg2Hv4OmIjQ7H8/hS5o9A9CFErYczU4pTJgl4umfRpkxZ8T08PTCYTSktLAQClpaUwmUywWq23XJeRkQGj0QiVirM+NF571xBOX7Zg9UOZCOGTq36vMCcBoodLJn3dpAVvNpuh1+uhVI5+UyqVSuh0OpjN5hkPR4FjX1U9lAoB3+bN1YAQGxWKwpx4fHisES63KHccugMuk6QZN2Rz4tNTzXhkYQriuC1wwHjigQz0DY7g8zOtckehO5h0PsVgMMBisUAURSiVSoiiiM7OThgMvHtOExu0OWF3uFFZVQ/7iIhH708dt/xuxMXRn78yZmqRnRyD9z+/hlWL06FQ8Ma5r5l0BB8fHw+j0YjKykoAQGVlJYxGI7Ra7uFNE7M73Dhp6sD+401IT4pCV58dZ2s7b/nhFvlEpL8SBAHPrJiDtq4hnDJ1yB2HbmNKUzSbNm3Czp07UVJSgp07d2Lz5s0AgHXr1uHixYsAgNOnT2P58uV466238Ic//AHLly/H4cOHZy45+YXLjVbYR9xYlKeTOwp5mVv0IDc9FvExGrx7sA6dVtu4H4M2p9wxg9qUlrzk5ORg9+7d496/ffv2sbeLi4vx5Zdfei8Z+T3R48G52i4kacNhSIiQOw552YhLRG1TL4yZWlRdaMeHRxuQFH/r/+eiPB2fdpURb7LSjDllsmDQ5kRRvo4PNgUwY5YWoWolztV2yR2FvoEFTzNC9EjYV1WP+BgNMg3RcsehGRSiUqIgJx717f3oGxyROw7dhAVPM+LLc63o6LFh8Tw9R+9BYP6cBCgVAs7VdcodhW7CgievE0UP/vBxLdJ0kchOjpE7Ds2CcI0aeRlxqG3qhc3hkjsOfYUFT173xblWtHcP46lHcjh6DyL35+ogeqQJd6Kk2cWCJ69yuT145+NaZCfH4P68RLnj0CyKjQpFTkoMLl7rhsPpljsOgQVPXrb/WCM6emz43reNHL0HoWKjHk63B9VXOYr3BSx48hqbw4U/fFKL+XMSsCifDzYFo4TYMGSnxODCtS6MOLkNhdxY8OQ1739+DQPDTvxN6X0cvQexxUY9nC4PLlzluni5seDJK3r67djz5XUsX5iCOWmxcschGd08ih+2c0WNnFjw5BW/23cJHo+E733bKHcU8gFL5o2O4j882iB3lKDGgqd7dvF6N74814bvrpg7bi8SCk7xMWHIz4jDwVMt47aIptnDgqd74hY9+M371dBpw/GXK+fKHYd8yJL7kgAAO/dfljlJ8GLB0z2prGpAU8cgXnyqAKE8a5VuEhUeglVL0nHobCvq2/rljhOUWPB0VwZtTtRc78bvPzJh/pwEZCdHj9sLnKc10ZNLMxEZFoLf/KkaHo8kd5ygM6X94Im+adjuwht/PA9IwP25iThXN35JXF5GnAzJyJeEa9T4b6Xz8MYfz+Oz081YtSRD7khBhSN4uiuHzozuN/PwgmRE8kAHmsCqxekwZmrxu30m9A9xO+HZxIKnaWuxDOK/PruKdH0UjJk8m5cmplAI+B9/uQA2hwtvV5rkjhNUWPA0LQ6nG7/YcQohagVWFKfxiVWakkxDNL7z2BwcPNWMYxfNcscJGix4mpZfv1+NFssg1pUVIjJMLXcc8iMVJfnISY3BG388h+4+u9xxggILnqbso6MN+PRUC/5qVS7uy46XOw75GbVKgZ+sLYbL7cFr/+8MRK6qmXEseJqSk5c68Ov3q1Fs1OOvn8iXOw75qZTESPzoO/NRc70Hv9tXI3ecgMdlkjSpuuZebP39aWSnxuKfvlcMpYLz7nT3Vi5OQ0N7P/78ZT0SY8Px9KM5ckcKWCx4mtCVJis2bT8ObXQoNrzwAMJC+SVD90YQBPzgqQJ099vxu3010EaHYvn9qXLHCkicoqE7unC1Cz/99VFER4Tg53/7MOKiNHJHogChVAj4h4pFmJcVj9d2ncFH3HVyRnA4Rrd18GQTtr1XjeSECGz50VLERbPcafrcomfC3ST/7rsLsH3vRWx7rxo9Aw5UPJEPBacAvYYFT7dwukT85k8X8fGJJiyYm4B/+t5iREfwSVW6OyMuEdXXJj6f9b9/dz52f3oV735Sh8sNVvzP54qQGBc2SwkDGwuexpgaevDGH8+jtXMIf7UqFxUl+byhSjNOkoDyVblISYzEOx/X4u/+z2f47oo5eGRhClTK0VnkMI0KUdwSY9pY8IS+wRHsOnAF+481QhcXhs3rHkIRD82mWTLiElHb1IuIMDWeXTkXn51uwc79V7Cvqh5L5iUhJzUWi416FvxdYMEHkUGbE3aHe+zn9hE3Dp5sxkfHG+FyefAXS9Lx10/kITEuXMaUFMxiIkPx9KM5aDQP4FiNGZ+cbMbRi2Z09AxjzbJs6LT82pwOFnwQsTvcOFvbCfuIGxeudqHmeg9GXCKyU2LwYEES4qI0cLknvil2A/d6p5kiCAKykmOQYYhGk3kAF691Y88X17Hni+vITY/FsgUpeHh+8m3L/puDmNsJpukeFnwQ6e6348tzrbjcaIVblJCTEoOiPN0t396Ep/cAAAkjSURBVChTuSkGcK93mnmKr4o+KzkGabpIXG7qRdWFNvxu3yX8bt8l5KXH4aFCAx6ab0ByQiSArwcxEynK07HgKTBIkgRTgxX7qupxrHp0F7+8jDjcn5vIpY/kNxLjwnFfTgL+8vG5MHcPo+pCG45Ut+PtD0x4+wMTMg3RWFpoQF5GHCRJ4i6nX2HBB6gRl4gvzraisqoeDe0DiAxT44kH0qHXhvOADvJrhoQIPLsyF8+uzEWn1YZjNWYcu2jGO5/UQpKAmMgQZCfHYE5aLBJjw4K67FnwAeLG3GNPvx2fn2nFl+fbMGx3IVUXie9/24gHCwwAgEv1PTInJfIenTYcZctzULY8B72DDhw80YxDZ1tx4WoXztV1ITYyFHPSYpGbFhuU/2JlwQcAx4gbn59uwYHjTWixDAIAslJiMD8nAcmJERAEAZfqezhvTgEtLkqDR4tSERURAofTjfq2ftQ19+H0ZQtOX7YgPkaD3LQ4pOujgmY1DgveT7ncozdDD51txfGLZjicIiLD1SjK12FeVjyfPqWgpglRYV5WPOZlxWPY7sK11j5cbekbnc6pMSM7JQaLjXoUG/WYmx4XsA/0seD9hFv0oL6tH1carai+1o0LV7vgcIqI0KjwaFEqFsxNxJDNGdTzjUS3ExGmxoK5iVgwNxEDwyOwOdy43GjF7k/r8O7BOkSFh6AoT4f7srXIz9QiPSk6YAp/SgXf0NCA9evXo6+vD7Gxsdi6dSsyMzNvuUYURfz85z/H4cOHIQgCfvjDH+LZZ5+dicyy6+6zo6fPDqdbhNPlwYhLhNMlQpIAQRhd3qXRqBChUUOpFKBUCFApFVB89V+lQrjlbUkafejI5nDBNuKG3eFG76ADXb12dPTY0GwZQItlCG7RAwDQa8OxojgNxfl6LMxNRIhaiU6rbdLlYUT+arJNy26Y7PmM6IhQLFuQgm8vzcKQ3YVL9T2ovtaNs7UWfHGuFQAQGqLEnNRYzMsaLfuMpCik6iKhVim98rnMpikV/MaNG1FRUYGysjLs3bsXGzZswI4dO265Zt++fWhubsbHH3+Mvr4+PP3003jooYeQmur7+zxLkoRhuwt9QyPoH3J+9d8R9A1+9eOWtx2wj8zOQz6CMDqvmKaPwppHdJibFgtjphYJsdyIiYKLN5/PuPm11CoFFuXrUJSXiIFhJzp6bLBYhzEw7MT7n18bO1ZQoRBgiI9Aqi4Sem04dNpw6L/6ERelQVREiE+O+ict+J6eHphMJrz11lsAgNLSUmzZsgVWqxVarXbsug8//BDPPvssFAoFtFotVq1ahf379+PFF1+cNIQojhZmR0fHtD+BYYcLRy60w+kS4fFIoz+Ar9/2SPBIo/91uj1wON0YcYoYcYpwON0YtLkwZHdCFG9/PmREmBrREaGIiQhBUlQIcpPCoFQq0Dc0ApVCgEolQKlQQKVUQBAASKObJyUlhKO9a3j095YkQAJEjwRJkuCRRv9SiY/WoLN39PBhtUoBtVoBtVIJtUqB0BAlIjQqCIKAgpwExMdoAEhwDPWgdWh8zp5+B3q6Jv4G6Ai1o6er/56v8eZrzeY1zBTYub3xWgnhQEK4CgU5SYiJDIWlZxhtXUNo7xpCW9cQGhqtOHXePu5fCoIAhGvUiAwLQVS4GqEho9/HISolVCoFQtRfv6366i8CQSFAEIAQlQqPLEhGmGb6M+Y3OvNGh37TpK9oNpuh1+uhVI7+80SpVEKn08FsNt9S8GazGcnJyWM/NxgMUy7srq4uAMDzzz8/peuJiALJ1nv89V1dXcjIyBj3fp+4yVpQUIBdu3YhMTFx7C8SIiKamCiK6OrqQkFBwW0/PmnBGwwGWCwWiKIIpVIJURTR2dkJg8Ew7rr29nbMnz8fwPgR/UQ0Gg2Ki4undC0REX3tdiP3GyY9kzU+Ph5GoxGVlZUAgMrKShiNxlumZwBg9erV2L17NzweD6xWKw4ePIiSkpJ7jE5ERHdLkCTp9ncXb3L9+nWsX78eAwMDiI6OxtatW5GdnY1169bhpZdeQmFhIURRxM9+9jMcOXIEALBu3TqUl5fP+CdARES3N6WCJyIi/zPpFA0REfknFjwRUYBiwRMRBSgWPBFRgGLBT8GJEydgNBqxc+dOuaP4lM2bN2P16tV46qmn8Nxzz+HixYtyR5JdQ0MDysvLUVJSgvLycjQ2NsodyWf09vZi3bp1KCkpwZo1a/DjH/8YVqtV7lg+5z//8z+Rl5eHurq6e34tFvwkhoaG8Oqrr2L58uVyR/E5y5cvx759+/DnP/8ZP/rRj/Dyyy/LHUl2NzbmO3DgACoqKrBhwwa5I/kMQRDw4osv4sCBA9i3bx/S0tLw6quvyh3Lp1y6dAnnz59HSkqKV16PBT+JX/ziF3jhhRcQF8fTkL5pxYoVUKvVAICFCxeio6MDHo9H5lTyubExX2lpKYDRjflMJhNHqV+JjY3FAw88MPbzhQsXor29XcZEvsXpdOJnP/sZNm3a5LXXZMFP4IsvvsDg4CBWr14tdxSft2vXLjz22GNQKIL3S2qijfnoVh6PB++88w4ef/xxuaP4jNdffx1PPfWUV7dY94nNxuTyne98544jiP379+O1114b2yY5GE3053P06NGxIvvggw+wb98+7Nq1azbjkR/bsmULwsPDsXbtWrmj+IRz586hpqYG//iP/+jV1w3qgv/Tn/50x4+dPn0aXV1dY6dS9fb24vPPP0dfXx9+/OMfz1ZEWU3053PDJ598gl/+8pd4++23kZCQMAupfNdUN+YLdlu3bkVTUxN+/etfB/W/+G526tQpXL9+HStXrgQwus/7Cy+8gH//93/HsmXL7v6FJZqSV155Rfr9738vdwyf8tlnn0krVqyQGhsb5Y7iM9auXSvt2bNHkiRJ2rNnj7R27VqZE/mW1157TVq7dq1ks9nkjuLTVqxYIdXW1t7z6wT1CJ7uzT//8z9DrVbjpZdeGnvf22+/HdQ3pDdt2oT169dj27ZtYxvz0airV6/iN7/5DTIzM/Hcc88BAFJTU/Hmm2/KnCxwcbMxIqIAxQkwIqIAxYInIgpQLHgiogDFgiciClAseCKiAMWCJyIKUCx4IqIAxYInIgpQ/x8EEkQtxJ8EtAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "sns.distplot(tfd.Normal(0., 1.).sample(1000, seed=random.PRNGKey(0)))\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_UTL6julDADw"
      },
      "source": [
        "`Distribution` methods are compatible with JAX transformations."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Itff7LYJDFKo"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "sns.distplot(jit(vmap(lambda key: tfd.Normal(0., 1.).sample(seed=key)))(\n",
        "    random.split(random.PRNGKey(0), 2000)))\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KM296i9CDS3w"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x = jnp.linspace(-5., 5., 100)\n",
        "plt.plot(x, jit(vmap(grad(tfd.Normal(0., 1.).prob)))(x))\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kWlbjWRv9lrC"
      },
      "source": [
        "Because TFP distributions are registered as JAX pytree nodes, we can write functions with distributions as inputs or outputs and transform them using `jit`, but they are not yet supported as arguments to `vmap`-ed functions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9QE5gvqL90hu"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "0.14389051 0.081832744\n"
          ]
        }
      ],
      "source": [
        "@jit\n",
        "def random_distribution(key):\n",
        "  loc_key, scale_key = random.split(key)\n",
        "  loc, log_scale = random.normal(loc_key), random.normal(scale_key)\n",
        "  return tfd.Normal(loc, jnp.exp(log_scale))\n",
        "random_dist = random_distribution(random.PRNGKey(0))\n",
        "print(random_dist.mean(), random_dist.variance())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aFSFOU9q254Y"
      },
      "source": [
        "### Transformed distributions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Oqif6lnT3Dei"
      },
      "source": [
        "Transformed distributions i.e. distributions whose samples are passed through a `Bijector` also work out of the box (bijectors work too! see below)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sZAEfYrl262w"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "dist = tfd.TransformedDistribution(\n",
        "    tfd.Normal(0., 1.),\n",
        "    tfb.Sigmoid()\n",
        ")\n",
        "sns.distplot(dist.sample(1000, seed=random.PRNGKey(0)))\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wVzuMoz2AHtM"
      },
      "source": [
        "### Joint distributions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b14tHrJAAKXx"
      },
      "source": [
        "TFP offers `JointDistribution`s to enable combining component distributions into a single distribution over multiple random variables. Currently, TFP offers three core variants (`JointDistributionSequential`, `JointDistributionNamed`, and `JointDistributionCoroutine`) all of which are supported in JAX. The `AutoBatched` variants are also all supported."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ThcymDXYAgCd"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "dist = tfd.JointDistributionSequential([\n",
        "  tfd.Normal(0., 1.),\n",
        "  lambda x: tfd.Normal(x, 1e-1)\n",
        "])\n",
        "plt.scatter(*dist.sample(1000, seed=random.PRNGKey(0)), alpha=0.5)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4CTLC5ZjAs_0"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "{'e': DeviceArray(3.376818, dtype=float32),\n",
              " 'm': DeviceArray(2.5449684, dtype=float32),\n",
              " 'n': DeviceArray(-0.6027825, dtype=float32),\n",
              " 'x': DeviceArray([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)}"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "joint = tfd.JointDistributionNamed(dict(\n",
        "    e=             tfd.Exponential(rate=1.),\n",
        "    n=             tfd.Normal(loc=0., scale=2.),\n",
        "    m=lambda n, e: tfd.Normal(loc=n, scale=e),\n",
        "    x=lambda    m: tfd.Sample(tfd.Bernoulli(logits=m), 12),\n",
        "))\n",
        "joint.sample(seed=random.PRNGKey(0))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ydOiznTJBldF"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "StructTuple(var0=DeviceArray(0.17315261, dtype=float32), var1=DeviceArray(-3.290489, dtype=float32), var2=DeviceArray(-3.1949058, dtype=float32), var3=DeviceArray([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], dtype=int32))"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "Root = tfd.JointDistributionCoroutine.Root\n",
        "def model():\n",
        "  e = yield Root(tfd.Exponential(rate=1.))\n",
        "  n = yield Root(tfd.Normal(loc=0, scale=2.))\n",
        "  m = yield tfd.Normal(loc=n, scale=e)\n",
        "  x = yield tfd.Sample(tfd.Bernoulli(logits=m), 12)\n",
        "\n",
        "joint = tfd.JointDistributionCoroutine(model)\n",
        "\n",
        "joint.sample(seed=random.PRNGKey(0))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IZ0mutV8-SQm"
      },
      "source": [
        "### Other distributions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qbu5BRnJ-V7p"
      },
      "source": [
        "Gaussian processes also work in JAX mode!"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8Cr6-Jyf_Rsu"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "k1, k2, k3 = random.split(random.PRNGKey(0), 3)\n",
        "observation_noise_variance = 0.01\n",
        "f = lambda x: jnp.sin(10*x[..., 0]) * jnp.exp(-x[..., 0]**2)\n",
        "observation_index_points = random.uniform(\n",
        "    k1, [50], minval=-1.,maxval= 1.)[..., jnp.newaxis]\n",
        "observations = f(observation_index_points) + tfd.Normal(\n",
        "    loc=0., scale=jnp.sqrt(observation_noise_variance)).sample(seed=k2)\n",
        "\n",
        "index_points = jnp.linspace(-1., 1., 100)[..., jnp.newaxis]\n",
        "\n",
        "kernel = tfpk.ExponentiatedQuadratic(length_scale=0.1)\n",
        "\n",
        "gprm = tfd.GaussianProcessRegressionModel(\n",
        "    kernel=kernel,\n",
        "    index_points=index_points,\n",
        "    observation_index_points=observation_index_points,\n",
        "    observations=observations,\n",
        "    observation_noise_variance=observation_noise_variance)\n",
        "\n",
        "samples = gprm.sample(10, seed=k3)\n",
        "for i in range(10):\n",
        "  plt.plot(index_points, samples[i], alpha=0.5)\n",
        "plt.plot(observation_index_points, observations, marker='o', linestyle='')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Kc4jP_sY_0CI"
      },
      "source": [
        "Hidden Markov models are also supported."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GoJ_tnaZ_1gT"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[3.       6.       7.5      8.249999 8.625001 8.812501 8.90625 ]\n"
          ]
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/tensorflow_probability/substrates/jax/distributions/hidden_markov_model.py:483: UserWarning: HiddenMarkovModel.log_prob in TFP versions < 0.12.0 had a bug in which the transition model was applied prior to the initial step. This bug has been fixed. You may observe a slight change in behavior.\n",
            "  'HiddenMarkovModel.log_prob in TFP versions < 0.12.0 had a bug '\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "-19.855635\n",
            "[ 1.3641367  0.505798   1.3626463  3.6541772  2.272286  15.10309\n",
            " 22.794212 ]\n"
          ]
        }
      ],
      "source": [
        "initial_distribution = tfd.Categorical(probs=[0.8, 0.2])\n",
        "transition_distribution = tfd.Categorical(probs=[[0.7, 0.3],\n",
        "                                                 [0.2, 0.8]])\n",
        "\n",
        "observation_distribution = tfd.Normal(loc=[0., 15.], scale=[5., 10.])\n",
        "\n",
        "model = tfd.HiddenMarkovModel(\n",
        "    initial_distribution=initial_distribution,\n",
        "    transition_distribution=transition_distribution,\n",
        "    observation_distribution=observation_distribution,\n",
        "    num_steps=7)\n",
        "\n",
        "print(model.mean())\n",
        "print(model.log_prob(jnp.zeros(7)))\n",
        "print(model.sample(seed=random.PRNGKey(0)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v5tN7E2ySKTa"
      },
      "source": [
        "A few distributions like `PixelCNN` are not supported yet due to strict dependencies on TensorFlow or XLA incompatibilities."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_QNMPVp07-YJ"
      },
      "source": [
        "## Bijectors"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XOCBtzf48GM0"
      },
      "source": [
        "Most of TFP's bijectors are supported in JAX today!"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aveBHt2y7_zT"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "DeviceArray(0., dtype=float32)"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "tfb.Exp().inverse(1.)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AAIGX7-T-pug"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[4. 4. 4. 4. 4.]\n",
            "[0. 0. 0. 0. 0.]\n"
          ]
        }
      ],
      "source": [
        "bij = tfb.Shift(1.)(tfb.Scale(3.))\n",
        "print(bij.forward(jnp.ones(5)))\n",
        "print(bij.inverse(jnp.ones(5)))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "IsqXLIz1-uFP"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[1. 0.]\n",
            " [0. 1.]]\n",
            "[0.6931472 0.5       0.       ]\n"
          ]
        }
      ],
      "source": [
        "b = tfb.FillScaleTriL(diag_bijector=tfb.Exp(), diag_shift=None)\n",
        "print(b.forward(x=[0., 0., 0.]))\n",
        "print(b.inverse(y=[[1., 0], [.5, 2]]))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "eb85mBpe-xZ7"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[1.3678794 1.3678794 1.3678794 1.3678794 1.3678794]\n"
          ]
        }
      ],
      "source": [
        "b = tfb.Chain([tfb.Exp(), tfb.Softplus()])\n",
        "# or:\n",
        "# b = tfb.Exp()(tfb.Softplus())\n",
        "print(b.forward(-jnp.ones(5)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EFPnn9fF8aKZ"
      },
      "source": [
        "Bijectors are compatible with JAX transformations like `jit`, `grad` and `vmap`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "snejb0gh8m-Z"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "DeviceArray([     -inf, 0.       , 0.6931472, 1.0986123], dtype=float32)"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "jit(vmap(tfb.Exp().inverse))(jnp.arange(4.))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Vp5AGkwB8tS-"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x = jnp.linspace(0., 1., 100)\n",
        "plt.plot(x, jit(grad(lambda x: vmap(tfb.Sigmoid().inverse)(x).sum()))(x))\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sT5iNTz-RjZH"
      },
      "source": [
        "Some bijectors, like `RealNVP` and `FFJORD` are not yet supported."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XTY99bpb_puj"
      },
      "source": [
        "## MCMC"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cuRf29WXCeMz"
      },
      "source": [
        "We've ported `tfp.mcmc` to JAX as well, so we can run algorithms like Hamiltonian Monte Carlo (HMC) and the No-U-Turn-Sampler (NUTS) in JAX."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dJaHRkDI_qY_"
      },
      "outputs": [],
      "source": [
        "target_log_prob = tfd.MultivariateNormalDiag(jnp.zeros(2), jnp.ones(2)).log_prob"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nzUl_pAZDwcw"
      },
      "source": [
        "Unlike TFP on TF, we are required to pass a `PRNGKey` into `sample_chain` using the `seed` keyword argument."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PSMURx2yC6aF"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "def run_chain(key, state):\n",
        "  kernel = tfp.mcmc.NoUTurnSampler(target_log_prob, 1e-1)\n",
        "  return tfp.mcmc.sample_chain(1000,\n",
        "      current_state=state,\n",
        "      kernel=kernel,\n",
        "      trace_fn=lambda _, results: results.target_log_prob,\n",
        "      seed=key)\n",
        "states, log_probs = jit(run_chain)(random.PRNGKey(0), jnp.zeros(2))\n",
        "plt.figure()\n",
        "plt.scatter(*states.T, alpha=0.5)\n",
        "plt.figure()\n",
        "plt.plot(log_probs)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F8ljmY_kEPkS"
      },
      "source": [
        "To run multiple chains, we can either pass a batch of states into `sample_chain` or use `vmap` (though we have not yet explored performance differences between the two approaches)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "swPzQ_OuETZt"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "states, log_probs = jit(run_chain)(random.PRNGKey(0), jnp.zeros([10, 2]))\n",
        "plt.figure()\n",
        "for i in range(10):\n",
        "  plt.scatter(*states[:, i].T, alpha=0.5)\n",
        "plt.figure()\n",
        "for i in range(10):\n",
        "  plt.plot(log_probs[:, i], alpha=0.5)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vtCVUJ2jWVj0"
      },
      "source": [
        "## Optimizers"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HUtYH1qZdsSH"
      },
      "source": [
        "TFP on JAX supports some important optimizers like BFGS and L-BFGS. Let's set up a simple scaled quadratic loss function."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "veOHaWtOeE0-"
      },
      "outputs": [],
      "source": [
        "minimum = jnp.array([1.0, 1.0])  # The center of the quadratic bowl.\n",
        "scales = jnp.array([2.0, 3.0])  # The scales along the two axes.\n",
        "\n",
        "# The objective function and the gradient.\n",
        "def quadratic_loss(x):\n",
        "  return jnp.sum(scales * jnp.square(x - minimum))\n",
        "\n",
        "start = jnp.array([0.6, 0.8])  # Starting point for the search."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NAhizt6QfJyj"
      },
      "source": [
        "BFGS can find the minimum of this loss."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WokahuxLfAyE"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Function evaluations: 5\n"
          ]
        }
      ],
      "source": [
        "optim_results = tfp.optimizer.bfgs_minimize(\n",
        "    value_and_grad(quadratic_loss), initial_position=start, tolerance=1e-8)\n",
        "\n",
        "# Check that the search converged\n",
        "assert(optim_results.converged)\n",
        "# Check that the argmin is close to the actual value.\n",
        "np.testing.assert_allclose(optim_results.position, minimum)\n",
        "# Print out the total number of function evaluations it took. Should be 5.\n",
        "print(\"Function evaluations: %d\" % optim_results.num_objective_evaluations)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6CaYRKQDfMAf"
      },
      "source": [
        "So can L-BFGS."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "O6p8aKmLfCHD"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Function evaluations: 5\n"
          ]
        }
      ],
      "source": [
        "optim_results = tfp.optimizer.lbfgs_minimize(\n",
        "    value_and_grad(quadratic_loss), initial_position=start, tolerance=1e-8)\n",
        "\n",
        "# Check that the search converged\n",
        "assert(optim_results.converged)\n",
        "# Check that the argmin is close to the actual value.\n",
        "np.testing.assert_allclose(optim_results.position, minimum)\n",
        "# Print out the total number of function evaluations it took. Should be 5.\n",
        "print(\"Function evaluations: %d\" % optim_results.num_objective_evaluations)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IqPKj0fEfOKB"
      },
      "source": [
        "To `vmap` L-BFGS, let's set up a function that optimizes the loss for a single starting point."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WtNGtdOlfTKV"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Function evaluations: [6 6 9 6 6 8 6 8 5 9]\n"
          ]
        }
      ],
      "source": [
        "def optimize_single(start):\n",
        "  return tfp.optimizer.lbfgs_minimize(\n",
        "      value_and_grad(quadratic_loss), initial_position=start, tolerance=1e-8)\n",
        "\n",
        "all_results = jit(vmap(optimize_single))(\n",
        "    random.normal(random.PRNGKey(0), (10, 2)))\n",
        "assert all(all_results.converged)\n",
        "for i in range(10):\n",
        "  np.testing.assert_allclose(optim_results.position[i], minimum)\n",
        "print(\"Function evaluations: %s\" % all_results.num_objective_evaluations)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GAeO8W2PiT8m"
      },
      "source": [
        "## Caveats"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nuuWzpFwiR6t"
      },
      "source": [
        "There are some fundamental differences between TF and JAX, some TFP behaviors will be different between the two substrates and not all functionality is supported. For example,\n",
        "\n",
        "\n",
        "*   TFP on JAX does not support anything like `tf.Variable` since nothing like it exists in JAX. This also means utilities like `tfp.util.TransformedVariable` are not supported either.\n",
        "*  `tfp.layers` is not supported in the backend yet, due to its dependence on Keras and `tf.Variable`s.\n",
        "*  `tfp.math.minimize` does not work in TFP on JAX because of its dependence  on `tf.Variable`.\n",
        "*   With TFP on JAX, tensor shapes are always concrete integer values and are never unknown/dynamic as in TFP on TF.\n",
        "*   Pseudorandomness is handled differently in TF and JAX (see appendix).\n",
        "*  Libraries in `tfp.experimental` are not guaranteed to exist in the JAX substrate.\n",
        "*  Dtype promotion rules are different between TF and JAX. TFP on JAX tries to respect TF's dtype semantics internally, for consistency.\n",
        "*  Bijectors have not yet been registered as JAX pytrees.\n",
        "\n",
        "\n",
        "To see the complete list of what is supported in TFP on JAX, please refer to the [API documentation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DHTL9SBqFuJq"
      },
      "source": [
        "## Conclusion"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EbLTaQ5UFwDg"
      },
      "source": [
        "We've ported a lot of TFP's features to JAX and are excited to see what everyone will build. Some functionality is not yet supported; if we've missed something important to you (or if you find a bug!) please reach out to us -- you can email [tfprobability@tensorflow.org](mailto:tfprobability@tensorflow.org) or file an issue on [our Github repo](https://github.com/tensorflow/probability)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "utaCcF7vmQPC"
      },
      "source": [
        "## Appendix: pseudorandomness in JAX"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OPx2BrR5mT4i"
      },
      "source": [
        "JAX's pseudorandom number generation (PRNG) model is *stateless*. Unlike a stateful model, there is no mutable global state that evolves after each random draw. In JAX's model, we start with a PRNG *key*, which acts like a pair of 32-bit integers. We can construct these keys by using `jax.random.PRNGKey`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "apUxosBpoFw1"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[0 0]\n"
          ]
        }
      ],
      "source": [
        "key = random.PRNGKey(0)  # Creates a key with value [0, 0]\n",
        "print(key)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "auAK011coID9"
      },
      "source": [
        "Random functions in JAX consume a key to *deterministically* produce a random variate, meaning they should not be used again. For example, we can use `key` to sample a normally distributed value, but we should not use `key` again elsewhere. Furthermore, passing the same value into `random.normal` will produce the same value."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "13CLYoUloPIe"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "-0.20584226\n"
          ]
        }
      ],
      "source": [
        "print(random.normal(key))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nUY7MRBeotJM"
      },
      "source": [
        "So how do we ever draw multiple samples from a single key? The answer is *key splitting*. The basic idea is that we can split a `PRNGKey` into multiple, and each of the new keys can be treated as an independent source of randomness."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1lc8QcSOo4Pi"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[4146024105  967050713] [2718843009 1272950319]\n"
          ]
        }
      ],
      "source": [
        "key1, key2 = random.split(key, num=2)\n",
        "print(key1, key2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2KCLSK2so8_v"
      },
      "source": [
        "Key splitting is deterministic but is chaotic, so each new key can now be used to draw a distinct random sample."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PUEfE6JApE_3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "0.14389051 -1.2515389\n"
          ]
        }
      ],
      "source": [
        "print(random.normal(key1), random.normal(key2))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WOgYcS9zpJG3"
      },
      "source": [
        "For more details about JAX's deterministic key splitting model, see [this guide](https://github.com/google/jax/blob/master/design_notes/prng.md)."
      ]
    }
  ],
  "metadata": {
    "accelerator": "GPU",
    "colab": {
      "collapsed_sections": [],
      "name": "TensorFlow_Probability_on_JAX.ipynb",
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
